LOGARITHMIC FORM TO EXPONENTIAL FORM

Converting logarithmic to exponential form :

log _a m = x -----> m = a^x

Example 1 :

Change the following from logarithmic form to exponential form.

log ₄64   =  3

Solution :

Given logarithmic form :

log ₄64  = 3 

Exponential form :

64  =  4³

Example 2 :

Obtain the equivalent exponential form of the following.

log₁₆2  =  1/4

Solution :

Given logarithmic form :

log₁₆2  =  1/4 

Exponential form :

 2  =  16^1/4

Example 3 :

Obtain the equivalent exponential form of the following.

log₅(1/25)  =  -2

Solution :

Given logarithmic form :

log₅(1/25)  =  -2

Exponential form :

 (1/25)  =  5^-2

Example 4 :

Obtain the equivalent exponential form of the following.

log₁₀0.1 =  -1

Solution :

Given logarithmic form :

log₁₀0.1 =  -1

Exponential form :

 0.1  =  10^-1

Example 5 :

Obtain the equivalent exponential form of the following.

log₆216 =  3

Solution :

Given logarithmic form :

log₆216 =  3

Exponential form :

 216  =  6³

Example 6 :

Obtain the equivalent exponential form of the following.

log₉3 =  1/2

Solution :

Given logarithmic form :

log₉3 =  1/2

Exponential form :

 3  =  9^(1/2)

Example 7 :

Obtain the equivalent exponential form of the following.

log₅1  =  0

Solution :

Given logarithmic form :

log₅1  =  0

Exponential form :

 1  =  5⁰

Example 8 :

Obtain the equivalent exponential form of the following.

log_√3 9  =  4

Solution :

Given logarithmic form :

log_√3 9  =  4

Exponential form :

 9  =  (√3)⁴

Example 9 :

Obtain the equivalent exponential form of the following.

log₆₄ (1/8)  =  -1/2

Solution :

Given logarithmic form :

log₆₄ (1/8)  =  -1/2

Exponential form :

 (1/8)  =  64^(-1/2)

Example 10 :

Obtain the equivalent exponential form of the following.

log_0.5 8  =  -3

Solution :

Given logarithmic form :

log_0.5 8  =  -3

Exponential form :

 8  =  0.5^-3

Example 11 :

Solve for x :

log₂x  =  1/2

Solution :

log₂x  =  1/2

Convert to exponential form. 

x  =  2^1/2

x  =  √2

Example 12 :

Solve for x :

log_1/5x  =  3

Solution :

log_1/5x  =  3

Convert to exponential form. 

x  =  (1/5)³

x  =  1³/5³

x  =  1/125

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.