Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 109

$2-\log_{10} {2.5}$

Divide $2$ to both sides of the equation to obtain: $10^{2-x}=\dfrac{5}{2}$ $10^{2-x}=2.5$ $\because a^y = x \text{ is equivalent to } log_a x = y$ $\therefore 10^{2-x}=2.5 \text{ is equivalent to } \log_{10} 2.5=2-x$ Solve the equation above to obtain: \begin{align*} \log_{10} 2.5&=2-x\\ x&=2-\log_{10} {2.5}\\ \end{align*}