Answer
(a) $x=\frac{5}{7}-\frac{\ln 15}{7\ln 2}$
(b) $x\approx 0.156158$
Work Step by Step
(a) We need to solve:
$2^{5-7x}=15$
We take the natural log of both sides and use log rules to simplify:
$(5-7x) \ln2 = \ln 15$
$5-7x=\frac{\ln 15}{\ln 2}$
$5-\frac{\ln 15}{\ln 2}=7x$
$x=\frac{5}{7}-\frac{\ln 15}{7\ln 2}$
(b) We solve using a calculator:
$x\approx 0.156158$
