# How do you solve (1.5)^(3x)=7.5?

Mar 17, 2016

$x \approx 1.66$

#### Explanation:

$1$. Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.

${1.5}^{3 x} = 7.5$

$\log \left({1.5}^{3 x}\right) = \log \left(7.5\right)$

$2$. Use the log property, ${\log}_{\textcolor{p u r p \le}{b}} \left({\textcolor{red}{m}}^{\textcolor{b l u e}{n}}\right) = \textcolor{b l u e}{n} \cdot {\log}_{\textcolor{p u r p \le}{b}} \left(\textcolor{red}{m}\right)$, to simplify the left side of the equation.

$\left(3 x\right) \log 1.5 = \log 7.5$

$3$. Solve for $x$.

$3 x = \log \frac{7.5}{\log} 1.5$

$x = \log \frac{7.5}{3 \log 1.5}$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} x \approx 1.66 \textcolor{w h i t e}{\frac{a}{a}} |}}}$