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} (10(1.5)^(3x))/(10)=(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} (3x\ln1.5)/(3\ln1.5)=(\ln 8)/(3\ln 1.5) \\ \\ x=(2.079)/(1.2164) \\ \\ x=1.71 \end{gathered}`

The value of x is 1.71

ANSWER:

x = 1.71