Respuesta :

McChuck
The answer is [tex]4^{-2}=\frac {1}{16}[/tex].

[tex]log_4 \frac {1}{16}=-2[/tex]

The subscript for log is 4, which is the base of the exponent. What the log function is equal to is the exponent, which is -2. Finally the number next to the log is the answer and that is [tex]\frac {1}{16}[/tex]
kudzordzifrancis
ANSWER

The exponential form is,

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]


EXPLANATION

The logarithmic expression given to us is

[tex] log_{4}( \frac{1}{16} ) = - 2[/tex]


We want to rewrite this in the exponential form,

We take the antilogarithm of both sides to base 4.


This implies that,

[tex] {4}^{log_{4}( \frac{1}{16} )} = {4}^{ - 2} [/tex]


Recall that,

[tex] {q}^{log_{q}( p )} = p[/tex]


This implies that,

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]


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