## College Algebra 7th Edition

$x \approx 2.60$
Take the natural log of both sides to obtain: $\ln{(2^{3x-5})} = \ln{7}$ Use the rule $\ln{(a^n)} = n\cdot\ln{a}$ to obtain: $(3x-5)\ln{2} = \ln{7}$ Divide $\ln{2}$ to both sides of the equation to obtain: $\dfrac{(3x-5)\ln2}{\ln2} = \dfrac{\ln7}{\ln2} \\3x-5=\dfrac{\ln7}{\ln2}$ Add $5$ on both sides of the equation to obtain: $3x=5+\dfrac{\ln7}{\ln2}$ Divide $3$ on both of the equation to obtain: $x = \dfrac{5+\frac{\ln7}{\ln2}}{3}$ Use a calculator to obtain: $x \approx 2.60$