ANSWER
[tex]x = \frac{ ln(832) }{ ln(4) } [/tex]
EXPLANATION
The given equation is
[tex] {4}^{x - 3} =13.[/tex]
[tex] ln({4}^{x - 3} )= ln(13)[/tex]
We use the power rule of logarithms to get:
[tex](x - 3) ln(4) = ln(13) [/tex]
Expand;
[tex]x ln(4) - 3 ln(4) = ln(13) [/tex]
Solve for x,
[tex]x ln(4)= ln(13) + 3 ln(4) [/tex]
[tex]x ln(4)= ln(13) + ln( {4}^{3} ) [/tex]
[tex]x ln(4)= ln(13) + ln(64) [/tex]
[tex]x ln(4)= ln(13 \times 64) [/tex]
[tex]x ln(4)= ln(832) [/tex]
[tex]x = \frac{ ln(832) }{ ln(4) } [/tex]
