Question

How do you write the equation `5^-3=1/125` in logarithmic form?

Answer 1

`log_5( 1/125)=-3`

Explanation:

Using the `color(blue)"laws of logarithms"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(log_b x=nhArrx=b^n)color(white)(2/2)|)))`

Consider `1/125=5^(-3)`

`rArrx=1/125,b=5" and " n=-3`

`rArr5^(-3)=1/125tolog_5(1/125)=-3`