Answer
(a). $x=\dfrac{2\log 5}{\log 175}$
(b). $x=0.623235$
Work Step by Step
$7^{x/2}=5^{1-x},$
(a).
$\frac{x}{2} \log 7=(1-x )\log 5,$
$\frac{x}{2-2x}=\frac{\log5}{\log7},$
$x=2\left(\frac{\log 5}{\log 7}\right)-2x\left(\frac{\log 5}{\log 7}\right),$
$x(1+2\frac{\log 5}{\log 7})=2\frac{\log 5}{\log 7},$
$$x=\frac{2\frac{\log 5}{\log 7}}{1+2\frac{\log5}{\log7}}=\frac{2\log 5}{\log 7+2\log 5}=\dfrac{2\log 5}{\log 175},$$
(b).
$x=0.623235$
