Answer
$x=2 - \log{2.5}$
Work Step by Step
Divide by 2 on both sides of the equation to obtain:
$\dfrac{2 \cdot 10^{2-x}}{2} = \dfrac{5}{2}
\\10^{2-x}=2.5$
Take the common logarithm of both sides to obtain:
$\log{(10^{2-x})}=\log{2.5}$
Note that $\log{(10^x)} = x$. Thus, the equation above is equivalent to:
$2-x=\log{2.5}$
Subtract by $2$ on both sides of the equation to obtain:
$2-x-2 = \log{2.5} - 2
\\-x = \log{2.5} - 2$
Multiply by $-1$ on both sides of the equation to obtain:
$-1(-x) = -1(\log{2.5}-2)
\\x = -\log{2.5} + 2
\\x=2 - \log{2.5}$