Answer
$x=\dfrac{5}{7}-\dfrac{\log15}{7\log2}\approx0.156158$
Work Step by Step
$2^{5-7x}=15$
Apply $\log$ to both sides of the equation:
$\log2^{5-7x}=\log15$
The exponent $5-7x$ can be taken down to multiply in front of its respective $\log$:
$(5-7x)\log2=\log15$
Solve for $x$:
$5-7x=\dfrac{\log15}{\log2}$
$7x=5-\dfrac{\log15}{\log2}$
$x=\dfrac{5}{7}-\dfrac{\log15}{7\log2}\approx0.156158$
