Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 36

$x=2.548$

$8(4^{6-2x})+13=41$ $8(4^{6-2x})=28$ $4^{6-2x}=\frac{28}{8}=\frac{7}{2}$ $\log_44^{6-2x}=\log_4\frac{7}{2}$ $6-2x=\log_4\frac{7}{2}$ $-2x=-6+\log_4\frac{7}{2}$ $x=\frac{-6}{-2}+\frac{\log_4\frac{7}{2}}{-2}=3-\frac{\ln\frac{7}{2}}{2\ln4}=2.548$