Question

Solve the equation. leave your answer in exact form. 4^(x-3)=13

Answer 1

`x = ( ln(832) )/( ln(4) )`

Step-by-step explanation

The given equation is

`{4}^(x - 3) =13.`

`ln({4}^(x - 3) )= ln(13)`

We use the power rule of logarithms to get:

`(x - 3) ln(4) = ln(13)`

Expand;

`x ln(4) - 3 ln(4) = ln(13)`

Solve for x,

`x ln(4)= ln(13) + 3 ln(4)`

`x ln(4)= ln(13) + ln( {4}^(3) )`

`x ln(4)= ln(13) + ln(64)`

`x ln(4)= ln(13 * 64)`

`x ln(4)= ln(832)`

`x = ( ln(832) )/( ln(4) )`