Answer
$x=\dfrac{2\log5}{\log7+2\log5}\approx0.623235$
Work Step by Step
$7^{x/2}=5^{1-x}$
Apply $\log$ to both sides of the equation:
$\log7^{x/2}=\log5^{1-x}$
The exponents $(x/2)$ and $(1-x)$ can be taken down to multiply in front of their respective logarithms:
$\dfrac{x}{2}\log7=(1-x)\log5$
Solve for $x$:
$\dfrac{x}{2}\log7=\log5-x\log5$
$x\log7=2\log5-2x\log5$
$x\log7+2x\log5=2\log5$
$x(\log7+2\log5)=2\log5$
$x=\dfrac{2\log5}{\log7+2\log5}\approx0.623235$
