Question

Type the correct answer in the box. Use numerals instead of words.What value of x satisfies this equation?

Answer 1

Given the equation:

$10(1.5)^{3x}=80^{}_{}$

Let's solve the equation for x.

Divide both sides by 10:

$\begin{gathered} \frac{10(1.5)^{3x}}{10}=\frac{80}{10} \\ \\ 1.5^{3x}=8 \end{gathered}$

Take the natural loagrithm of both sides:

$\begin{gathered} \ln 1.5^{3x}=\ln 8 \\ \\ 3x\ln 1.5=\ln 8 \end{gathered}$

DIvide both sides by 3ln1.5:

$\begin{gathered} \frac{3x\ln1.5}{3\ln1.5}=\frac{\ln 8}{3\ln 1.5} \\ \\ x=\frac{2.079}{1.2164} \\ \\ x=1.71 \end{gathered}$

The value of x is 1.71

ANSWER:

x = 1.71