### Home > PC3 > Chapter 13 > Lesson 13.2.2 > Problem13-80

13-80.

Solve for $x$ in each of the following equations.

1. $3^{x} = 7$

Take the log of both sides.

1. $9^{2x}=27^{x-2}$

$(3^2)^{2x}=(3^3)^{x-2}$

1. $\log_2\left(\log_9\left(\log_3\left(x\right)\right)\right)=-1$

$2^{-1}=\log_9\left(\log_3\left(x\right)\right)$

$\log_9(\log_{3}(x))=\frac{1}{2}$

$9^{1/2}=\log_3(x)$

$\log_{3}(x) = 3$

1. $\left(x-3\right)\left(\ln\left(x\right)-2\right)=0$

$x-3=0$ or $\ln\left(x\right)-2=0$