Question

solve for x.
3 ln(5x) = 12
do not round any intermediate computations, and round your answer to the nearest h
x =

Explanation:

Step1: Divide both sides by 3

To isolate the natural logarithm term, we divide both sides of the equation \(3\ln(5x) = 12\) by 3. This gives us \(\ln(5x)=\frac{12}{3} = 4\).

Step2: Exponentiate both sides

Since the natural logarithm \(\ln\) is the inverse of the exponential function \(e^x\), we exponentiate both sides with base \(e\) to get rid of the logarithm. So, \(e^{\ln(5x)}=e^{4}\). By the property of logarithms and exponents, \(e^{\ln(a)} = a\), so this simplifies to \(5x = e^{4}\).

Step3: Solve for x

Now, we divide both sides by 5 to solve for \(x\). So, \(x=\frac{e^{4}}{5}\). Calculating \(e^{4}\approx54.59815\), then \(\frac{54.59815}{5}=10.91963\). Rounding to the nearest hundredth (assuming the problem meant nearest hundredth as it was cut off), we get \(x\approx10.92\).

Answer:

\(x\approx10.92\)