Answer
(a) $x=\frac{1}{3}$
(b) $x=\frac{11}{3}$
(c) $x=-2$
Work Step by Step
We simplify as follows:
(a) $64^{x}=4$
$(4^{3})^{x}=4^{1}$
$4^{3x}=4^{1}$
$3x=1$
$x=\frac{1}{3}$
(b) $125^{x-3}=25$
$(5^{3})^{x-3}=5^{2}$
$5^{3x-9}=5^{2}$
$3x-9=2$
$3x=11$
$x=\frac{11}{3}$
(c) $\frac{1}{81}=3^{2x}$
$3^{-4}=3^{2x}$
$2x=-4$
$x=-2$
