Home > Precalculus > Logarithm-- Inverse of an Exponential Function

How do you evaluate #log_4 4^-0.38#?

Answer 1

Ariana Alvarez

I got #-0.38#

With the exponent placed in front of the log, we can write:

#-0.38log_4(4)=#

but #log_4(4)=1# (from the definition of log) so you get:

#-0.38*1=-0.38#

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Answer 2

Liam Brennan

To evaluate log_4 4^-0.38, you can use the property of logarithms which states that log_b (b^x) = x for any base b and any real number x. Therefore, log_4 4^-0.38 = -0.38.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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