LOGARITHMS EXAM QUESTIONS PDF log. 2 log x y. = + .

MAT 163 - Surds Indices

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5. SURDS AND LOGARITHMS

Rationalizing Factor: When the product of two surds is a rational number then each surd is called. Rationalizing Factor (R.F.). • Law of Surds and Exponents.

EXPONENTS AND LOGARITHMS

= giving your answers in simplified surd form. Make sure you check your answers by substituting them into the original equation. 14. Solve the equation 25.

AMath - Indices Surds and Logarithms Notes.pdf

%20Surds%20and%20Logarithms%20Notes.pdf

Maths Module 4 - Powers Roots and Logarithms

surds. This process is explained on the next page. 5. Your Turn: Which of the following are surds? a. √1 b. √2 c. √3 d. √4 e. √9 f. √2. 3 g. √8. 3 h ...

Cambridge IGCSE 0580 Mathematics syllabus for examination in

Knowledge of logarithms is not required. C2.5 Equations. Notes and examples. 1 1 Understand and use surds including simplifying expressions. 2 Rationalise ...

Introduction to Exponents and Logarithms Christopher Thomas

exponential form and we call b the base and n the exponent

Quick Start Guide (fx-991EX/fx570EX)_CASIO

Calculate 13 different one-variable statistics and apply linear

N3-Answers-Exponents Surd Logarithms

maTH(ə)ˈma ks. Exponents surds and logarithms. Page 2. N3-Exponents

Properties of Exponents and Logarithms

Properties of Logarithms (Recall that logs are only defined for positive values of x.) For the natural logarithm For logarithms base a. 1. lnxy = lnx + lny. 1.

Grade-11-12-Mathematics-Exponents-Surds-and-Logs-.pdf

Simplify expressions involving rational exponents. Unit 2. • Simplify expressions involving surds. Unit 3. • Revise the logarithmic notation and logarithm

LOGARITHMS EXAM QUESTIONS

log. 2. 4 x y. = Question 7 (**+). An exponential curve has equation c) Determine as an exact simplified surd

N3-Answers-Exponents Surd Logarithms

maTH(?)?ma ks. Exponents surds and logarithms. Page 2. N3-Exponents

Maths Module 4 - Powers Roots and Logarithms

5. Roots. 6. Root Operations. 7. Simplifying Fractions with Surds. 8. Fraction Powers/Exponents/Indices. 9. Logarithms. 10. Helpful Websites. 11. Answers

5. SURDS AND LOGARITHMS

Rationalizing Factor: When the product of two surds is a rational number then each surd is called. Rationalizing Factor (R.F.). • Law of Surds and Exponents.

Indices Surds and Logarithms

%20Surds%20and%20Logarithms%20Notes.pdf

Logarithms

solve simple equations requiring the use of logarithms. Contents. 1. Introduction Write the following using logarithms instead of powers a) 82 = 64.

N3-Questions-Exponents Surds Logarithms

N3 Math Exam Paper. Exponents surds and logarithms. maTH(?)?ma ks. Page 2. N3-Exponents

Worksheet 2.7 Logarithms and Exponentials

Logs have some very useful properties which follow from their definition and the equivalence of the logarithmic form and exponential form. Some useful

Created by T. Madas

LOGARITHMS

EXAM

QUESTIONS

Created by T. Madas

Question 1 (**)

Show clearly that

1log 36 log 256 2log 48 log 42a a a a+ - = -.

proof

Question 2 (**)

Simplify

2 2log 5 log 1.6+,

giving the final answer as an integer. 3

Question 3 (**+)

Given that 2px= and 4qy=, show clearly that

32log ( ) 3 2x y p q= +.

proof

Created by T. Madas

Question 4 (**+)

Simplify each of the following expressions, giving the final answer as an integer. a) 2 2log 3 log 24-. b) 21log 4loga aaa

Ä Ô-Å ÕAE Ö, 0a>, 1a≠.

Full workings, justifying every step, must support each answer. 3-, 6

Question 5 (**+)

Given that 2logy x=, write each of the following expressions in terms of y. a) 22logx b) ()22log 8x

2y, 3 2y+

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Question 6 (**+)

Given that 24 10xy= × express x in terms of y, giving an exact simplified answer in terms of logarithms base 10. ()101 1log2 4x y=

Question 7 (**+)

An exponential curve has equation

xy ab=, x??, where a and b are non zero constants. Make x the subject of the above equation, giving the final answer in terms of logarithms base 10. log log log y axb-=

Created by T. Madas

Question 8 (**+)

Solve the following logarithmic equation

10 10 102log log 3 log 75x+ =.

5, 5x x= ≠ -

Question 9 (**+)

Solve the following logarithmic equation

log log ( 3) log 10a a ax x+ - =.

C2H, 5, 2x x= ≠ -

Created by T. Madas

Question 10 (***)

An exponential curve C has equation

3xy=, x??.

a) Sketch the graph of C. b) Solve the equation 23y=, giving the answer correct to 3 significant figures.

C2B, 0.369

Created by T. Madas

Question 11 (***)

Given that

log 4ap= and log 5aq=, express each of the following logarithms in terms of p and q. a) log 100a b) log 0.4a

The final answers may not contain any logarithms.

C2G, 2p q+, 12p q-

Question 12 (***)

Solve the following logarithmic equation

5 5log (4 7) log 2t t+ - =.

C2L, 13t=

Created by T. Madas

Question 13 (***)

Given that

2log 3p= and 2log 5q=,

express each of the following logarithms in terms of p and q. a) 2log 45 b) 2log 0.3

The final answers may not contain any logarithms.

MP1-N, 2p q+, 1p q- -

Created by T. Madas

Question 14 (***)

Solve each of the following equations, giving the final answers correct to three significant figures, where appropriate. a) 7 10x=. b) 2 2

9loglogyy=.

C2J, 1.18x≈, 1, 88y=

Question 15 (***)

Solve the following logarithmic equation for x.

2log ( 10) log 2log 3a a ax x- - =.

10, 1x x= ≠ -

Created by T. Madas

Question 16 (***)

Solve the following logarithmic equation for x.

2log log 18 log ( 4)a a ax x= + -.

C2C, 6, 12x=

Question 17 (***)

Solve the following logarithmic equation

2 2log (2 1) 2 logz z+ = +.

C2O, 12z=

Created by T. Madas

Question 18 (***)

Solve the following logarithmic equation for y.

2log log (5 24) log 4a a ay y- - =.

8, 12x=

Question 19 (***)

It is given that x satisfies the logarithmic equation log 2(log log 2)a a ax k= -, where

0k>, 0a>, 1a≠.

a) Find x in terms of k, giving the answer in a form not involving logarithms.

Suppose instead that

x satisfies ()log 5 1 4 log 3x xy+ = + where

0x>, 1x≠ and 0y>, 1y≠.

b) Solve the above equation expressing y in terms of x, giving the answer in a form not involving logarithms. 2 4 kx=, 43 1
5 xy-=

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Question 20 (***)

Solve the following logarithmic equation

5log (125 ) 4x=.

5x=

Question 21 (***)

Solve the following logarithmic equation

()5 51 2log log 16 3x x+ = -.

13,5x x= =

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Question 22 (***)

Every £1 invested in a saving scheme gains interest at the rate of 5% per annum so that the total value of this £1 investment after t years is £y.

This is modelled by the equation

1.05ty=, 0t≥.

Find after how many years the investment will double.

14.2t≈

Question 23 (***)

Solve each of the following logarithmic equations. a) log 16 log 9 2x x= +. b) log 27 3 log 8y y= +.

4 4,3 3x x= ≠ -, 32y=

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Question 24 (***)

Solve each of the following equations, giving the final answers correct to three significant figures, where appropriate. a) 2 3 900x× =. b) ()()2 2log 7 1 3 log 1y y- = + -.

C2P, 5.56x≈, 7y=

Question 25 (***+)

Simplify fully

1 2log 3 log 4n n+ +,

giving the final answer as a single logarithm. log (36 )nn

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Question 26 (***+)

Solve each of the following exponential equations, giving the final answers correct to

3 significant figures.

a) 2 1 3005 4x-=. b) 11022 y y

C2M, 130x≈, 1.16y≈

Question 27 (***+)

Solve the following logarithmic equation

2 22 2log ( 4 3) 4 log ( )w w w w+ + = + +, 1w≠ -.

15w=

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Question 28 (***+)

Solve the following exponential equation

1 1 6 2 xÄ Ô=Å ÕAE Ö, giving the answer as single logarithm of base 2.

2 2log 6 1 log 3x= = +

Question 29 (***+)

Solve the following simultaneous logarithmic equations ()22log 0xy= ()22log 3x y=.

C2U, 14,2x y= =

Created by T. Madas

Question 30 (***+)

Solve the following logarithmic equation

3 32log 1 log 7t t= +.

21, 0t t= ≠

Question 31 (***+)

Solve the following logarithmic equation

3 3log 8 3log 3t- =.

C2E, 23t=

Created by T. Madas

Question 32 (***+)

Solve the following logarithmic equation

5 5log (4 ) 2log 1w w- - =.

C2A, 4, 15w w= ≠ -

Question 33 (***+)

Simplify fully the following logarithmic expression, showing clearly all the workings. ()()()log 10 3 10 log 10 90 90 log 10 90 90+ + + + + - +. 1

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Question 34 (***+)

Solve the following logarithmic equation

2 2 2log log (3 4) 2log (3 4)y y y+ + = -.

24,3y y= ≠

Question 35 (***+)

Solve the following logarithmic equation

2 2log (6 ) 3 logx x- = -.

2, 4x=

Created by T. Madas

Question 36 (***+)

Solve the following logarithmic equation

4 3log log 9x=.

16x=

Question 37 (***+)

Solve each of the following equations.

1222 3 23.43x+× =.

b) ()()()5 5 5log 2 log 4 3 2log 2 1y y y+ + - = +.

0.480x≈, 7y=

Created by T. Madas

Question 38 (***+)

The population P of a certain town in time t years is modelled by the equation

10 , 0ktP A t= × ≥,

where

A and k are non zero constants.

When

3t=, 19000P= and when 6t=, 38000P=.

Find the value of

A and the value of k, correct to 2 significant figures.

C2V, 9500, 0.10A k= =

Question 39 (***+)

Solve the following logarithmic equation

3 32log log ( 2) 2x x- - =.

C2F, 3, 6x=

Created by T. Madas

Question 40 (***+)

Solve the following logarithmic equation

2 12 3log 4 log 27x x-=.

3x= -

Question 41 (***+)

Given that 0a≠, 0b≠, 0y≠ and

()22 log 3log 2loga a ab y a y+ + =, express y in terms of a and b, in a form not involving logarithms. 2ayb=

Created by T. Madas

Question 42 (***+)

22log 1 log(10 )xx yy

Ä Ô- =Å ÕAE Ö, 0x≠, 0y≠.

Find the exact value of

y. 31
100y=

Question 43 (***+) non calculator

The points P and Q lie on the curve with equation

2 26log log 7y x= -, 0x>.

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[PDF] LOGARITHMS EXAM QUESTIONS log. 2 log x y. = + .

Created by T. Madas

Created by T. Madas

LOGARITHMS

QUESTIONS

Created by T. Madas

Created by T. Madas

Question 1 (**)

Show clearly that

1log 36 log 256 2log 48 log 42a a a a+ - = -.

Question 2 (**)

Simplify

2 2log 5 log 1.6+,

Question 3 (**+)

Given that 2px= and 4qy=, show clearly that

32log ( ) 3 2x y p q= +.

Created by T. Madas

Created by T. Madas

Question 4 (**+)

Ä Ô-Å ÕAE Ö, 0a>, 1a≠.

Question 5 (**+)

2y, 3 2y+

Created by T. Madas

Created by T. Madas

Question 6 (**+)

Question 7 (**+)

An exponential curve has equation

Created by T. Madas

Created by T. Madas

Question 8 (**+)

Solve the following logarithmic equation

10 10 102log log 3 log 75x+ =.

5, 5x x= ≠ -

Question 9 (**+)

Solve the following logarithmic equation

C2H, 5, 2x x= ≠ -

Created by T. Madas

Created by T. Madas

Question 10 (***)

An exponential curve C has equation

3xy=, x??.

C2B, 0.369

Created by T. Madas

Created by T. Madas

Question 11 (***)

Given that

The final answers may not contain any logarithms.

C2G, 2p q+, 12p q-

Question 12 (***)

Solve the following logarithmic equation

5 5log (4 7) log 2t t+ - =.

C2L, 13t=

Created by T. Madas

Created by T. Madas

Question 13 (***)

Given that

2log 3p= and 2log 5q=,

The final answers may not contain any logarithms.

MP1-N, 2p q+, 1p q- -

Created by T. Madas

Created by T. Madas

Question 14 (***)

9loglogyy=.

C2J, 1.18x≈, 1, 88y=

Question 15 (***)

Solve the following logarithmic equation for x.

2log ( 10) log 2log 3a a ax x- - =.

10, 1x x= ≠ -

Created by T. Madas

Created by T. Madas

Question 16 (***)

Solve the following logarithmic equation for x.

2log log 18 log ( 4)a a ax x= + -.

C2C, 6, 12x=

Question 17 (***)

Solve the following logarithmic equation

2 2log (2 1) 2 logz z+ = +.

C2O, 12z=

Created by T. Madas

Created by T. Madas