Question

log4 (x - 7) = 3
solve for x

Answer 1

Firstly we apply the rule: $a=\log _b\left(b^a\right)$:
$\log _4\left(x-7\right)=3 \\\log _4\left(x-7\right)=\log _4\left(64\right)$

When the logarithms have same base, the following rule applies: $\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right) \Rightarrow f\left(x\right)=g\left(x\right)$.

And now we simply solve the linear equation:
$x-7=64 \\x=71$.

Answer 2

I know you all might want the steps too but the way i used in solving it is pretty long, but the answer is
2log2(x−7)=3

log2(x−7)=​3/2

x−7=​3/2log2​​​

x−7=3/​2log2​​

$x = \frac{3}{2 log(2) }+ 7$
i hope this help