Write log2 (1/8) = -3 in exponential form

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Question from Jaime, a student:

how do you write log2 (1/8) = -3 in exponential form?

the 1/8 is a fraction and the 2 is a base of 2

thanks
jaime

Jamie,

For any positive number a, 2^log₂(a) = a. Thus in your equation if you raise both sides to the power of 2 you get

2^log₂(1/8) = 2^-3 or

1/8 = 2^-3

This technique is particularly useful in solving some equations. For example

For what number x is log₂(x + 1) = 5?

Applying the same technique of raising both sides to the power of 2 this equation becomes

2^log₂(x+1) = 2⁵

which simplifies to

x + 1 = 2⁵ = 32

x = 31.

Penny

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