Answer
$x = \dfrac{\log{(\frac{3}{8})} + 7}{2} $
Work Step by Step
Divide both sides of the equation by 8 to obtain:
$\dfrac{8 \cdot 10^{2x-7}}{8} = \dfrac{3}{8}
\\10^{2x-7}=\dfrac{3}{8}$
Take the common logarithm of both sides to obtain:
$\log{(10^{2x-7})}=\log{(\frac{3}{8})}$
Note that $\log{(10^x}) = x$. Thus, the equation above is equivalent to:
$2x-7=\log{(\frac{3}{8})}$
Add $7$ to both sides of the equation to obtain:
$2x-7+7 = \log{(\frac{3}{8})} + 7
\\2x = \log{(\frac{3}{8})} + 7$
Divide by 2 on both sides of the equation to obtain:
$\dfrac{2x}{2} = \dfrac{\log{(\frac{3}{8})} + 7}{2}
\\x = \dfrac{\log{(\frac{3}{8})} + 7}{2} $
