type the correct answer in the box. use numerals instead of words. what value of x satisfies this equation…

Explanation:

Step1: Isolate the exponential term

Divide both sides of the equation $10(1.5)^{3x}=80$ by 10. We get $(1.5)^{3x}=\frac{80}{10}=8$.

Step2: Take the natural - logarithm of both sides

$\ln((1.5)^{3x})=\ln(8)$. Using the property of logarithms $\ln(a^{b}) = b\ln(a)$, we have $3x\ln(1.5)=\ln(8)$.

Step3: Solve for x

First, find $\ln(8)\approx2.0794$ and $\ln(1.5)\approx0.4055$. Then $3x=\frac{\ln(8)}{\ln(1.5)}=\frac{2.0794}{0.4055}\approx5.13$. Divide both sides by 3: $x=\frac{5.13}{3}\approx1.71$.

Answer:

$1.71$