Answer
$$x \approx 2.602452$$
Work Step by Step
$Use$ $a$ $calculator$ $to$ $find$ $the$ $solution$ $of$ $the$ $equation,$ $rounded$ $to$ $six$ $decimal$ $places:$
$2^{3x-5} = 7$
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
$$x \approx 2.602452$$
