# SOLVING LOGARITHMIC EQUATIONS WITH VARIABLES WORKSHEET

## About "Solving logarithmic equations with variables worksheet"

Solving logarithmic equations with variables worksheet :

Here we are going to see some practice questions on solving logarithmic equations.

Before going to look into the practice questions you may visit the page "Solving logarithmic equations with variables "

## Solving logarithmic equations with variables worksheet - Practice questions

(1)  Solve the following equation

log5 x   =  -3

(2)  Solve the following equation

x  =  log1/4 64

(3)  Solve the following equation

logx 8  =  2

(4) Solve the following equation

log2 x   =  1/2

(5)  Solve the following equation

log1/5 x   =  3

(6)  Solve the following equation

log3 y   =  -2

(7)  Solve the following equation

logx 125 √5  =  7

(8)  Solve the following equation

logx 0.001  =  -3

(9)  Solve the following equation

x + 2 log27 9  =  0

(10)  Solve the following equation

logx 71/6  =  1/3

## Solving logarithmic equations with variables worksheet - Solution

Question 1 :

Solve the following equation

log5 x   =  -3

Solution :

Given logarithmic form :

log5 x   =  -3

Exponential form :

x   =  5-3

x  =  1/53

x  =   1/125

Hence the value of x is 1/125.

Question 2 :

Solve the following equation

x  =  log1/4 64

Solution :

Given logarithmic form :

x  =  log1/4 64

Exponential form :

(1/4)x   =  64

(4-1)x  =  43

4-x  =   43

-x  =  3

Hence the value of x is -3.

Question 3 :

Solve the following equation

logx 8  =  2

Solution :

Given logarithmic form :

logx 8  =  2

Exponential form :

8  =  x2

√8  =  x

x  =  2√2

Hence the value of x is 2√2.

Question 4 :

Solve the following equation

log2 x   =  1/2

Solution :

Given logarithmic form :

log2 x   =  1/2

Exponential form :

x   =  21/2

x  =  √2

Hence the value of x is √2.

Question 5 :

Solve the following equation

log1/5 x   =  3

Solution :

Given logarithmic form :

log1/5 x   =  3

Exponential form :

x   =  (1/5)3

x  =  13/53

x  =  1/125

Hence the value of x is 1/125.

Question 6 :

Solve the following equation

log3 y   =  -2

Solution :

Given logarithmic form :

log3 y   =  -2

Exponential form :

y   =  3-2

y  =  1/32

y  =  1/9

Hence the value of y is 1/9.

Question 7 :

Solve the following equation

logx 125 √5  =  7

Solution :

Given logarithmic form :

logx 125 √5  =  7

Exponential form :

125 √5  =  x7

5 ⋅ 5 ⋅ 5 ⋅ √5  =  x7

Every 5 can be expressed as the product of ⋅ 5

√5 ⋅ √5 ⋅ √5 ⋅ √5 ⋅ √5 ⋅ √5 ⋅ √5  =  x7

√57  =  x7

Since the powers are equal, the value of bases will be equal.

x  =  √5

Hence the value of x is √5.

Question 8 :

Solve the following equation

logx 0.001  =  -3

Solution :

Given logarithmic form :

logx 0.001  =  -3

Exponential form :

0.001  =  x-3

1/1000  =  x-3

(1/10)3  =  x-3

(10-1)3  =  x-3

10-3  =  x-3

Hence the value of x is 10.

Question 9 :

Solve the following equation

x + 2 log27 9  =  0

Solution :

x + 2 log27 9  =  0

x  =  - 2 log27 9

x  =  log27 9-2

x  =  log27 9-2

27x  =  9-2

Express 27 and 9 as the exponent of 3.

(33)x  =  9-2  ==>  33x  =   (32)-2

33x  =   3-4

3x  =  -4

x  =  -4/3

Hence the value of x is -4/3.

Question 10 :

Solve the following equation

logx 71/6  =  1/3

Solution :

logx 71/6  =  1/3

71/6  =  x1/3

71/(23)  =  x1/3

(71/2)(1/3)  =  x1/3

(7)(1/3)  =  x1/3

x  =  √7

Hence the value of x is √7.

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