Question

Evaluate the log without a calculator ( Show your work )


`log_(25) (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

`\log_(25)((1)/(5))=-(1)/(2)`

Explanation:

Let

`\log_(25)((1)/(5))=x`

We rewrite as an exponential equation to obtain;

`(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=-(1)/(2)`