Question

the real solution of the equation $3e^x = 12$ is:
a. $ln 4$
b. $3ln 12$
c. $4^e$
d. $\frac{ln 12}{3}$
\bigcirc a
\bigcirc b
\bigcirc c
\bigcirc d

Explanation:

Step1: Isolate the exponential term

Divide both sides of the equation \(3e^{x}=12\) by 3.
\(\frac{3e^{x}}{3}=\frac{12}{3}\)
Simplify to get \(e^{x} = 4\).

Step2: Apply the natural logarithm

Take the natural logarithm of both sides. Recall that \(\ln(e^{a})=a\) for any real number \(a\).
Taking \(\ln\) of both sides: \(\ln(e^{x})=\ln(4)\)
By the property of logarithms, \(\ln(e^{x}) = x\), so \(x=\ln(4)\).

Answer:

A. \(\ln 4\)