## Precalculus: Mathematics for Calculus, 7th Edition

$$x \approx 2.602452$$
$Use$ $a$ $calculator$ $to$ $find$ $the$ $solution$ $of$ $the$ $equation,$ $rounded$ $to$ $six$ $decimal$ $places:$ $2^{3x-5} = 7$ Write the equation in logarithmic form: $b^c = a \rightarrow \log_b a = c$ $2^{3x-5} = 7 \rightarrow \log_2 7 = 3x-5$ $$\log_2 7 = 3x-5$$ Solve for x add 5 to both sides $$5+\log_2 7 = 3x-5+5$$ $$5+\log_2 7 = 3x$$ Divide both sides by 3 $$\frac{5+\log_2 7}{3} = \frac{3x}{3}$$ $$x = \frac{5+\log_2 7}{3}$$ Plug into calculator $$x = 2.602451640685868$$ Round to six decimal places $$x \approx 2.602452$$