Question

What is the solution to the equation below? Round your answer to two

Answer 1

Option D:

x = 2.06

Solution:

Given equation is $2^{3x}=73$.

To find the value of x:

If f(x) = g(x), then $\ln (f(x))=\ln (g(x))$.

Raise ln on both sides of the equation.

$\ln 2^{3x}=\ln73$

Using log rule: $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$

$3 x \ln (2)=\ln 73$

Divide by 3ln(2) on both sides.

$\frac{3 x \ln (2)}{3 \ln (2)}=\frac{\ln (73)}{3 \ln (2)}$

$x=\frac{\ln (73)}{3 \ln (2)}$

x = 2.0632

x = 2.06

Hence Option D is the correct answer.