Question

Evaluate the log without a calculator ( Show your work )

$log_{25} \frac{1}{5}$

Answer 1

log 1/5 base 25
25^x=1/5
thinking of number that satisfy it
it is =-1/2

Answer 2

Answer:

$\log_{25}(\frac{1}{5})=-\frac{1}{2}$

Step-by-step explanation:

Let

$\log_{25}(\frac{1}{5})=x$

We rewrite as an exponential equation to obtain;

$\frac{1}{5}=25^x$

We rewrite both sides of the equation as an index number to base 5.

$5^{-1}=5^{2x}$

Since the bases are the same, we equate the exponents to obtain;

$-1=2x$

Divide both sides by 2;

$x=-\frac{1}{2}$