Question

question 6 of 10
what is the solution to the equation below? round your answer to two decimal places.
$2^{3x} = 73$
a. $x = 0.05$
b. $x = 6.19$
c. $x = 2.06$
d. $x = 0.48$

Explanation:

Step1: Take log of both sides

Take the natural logarithm (ln) of both sides of the equation \(2^{3x} = 73\). We get \(\ln(2^{3x})=\ln(73)\).

Step2: Use logarithm power rule

Using the power rule of logarithms \(\ln(a^b)=b\ln(a)\), the left - hand side becomes \(3x\ln(2)=\ln(73)\).

Step3: Solve for x

First, we can express \(x\) as \(x = \frac{\ln(73)}{3\ln(2)}\).
We know that \(\ln(73)\approx4.2904\) and \(\ln(2)\approx0.6931\).
Substitute these values into the formula for \(x\):
\(3\ln(2)=3\times0.6931 = 2.0793\)
\(x=\frac{4.2904}{2.0793}\approx2.06\) (rounded to two decimal places)

Answer:

C. \(x = 2.06\)