Question

1. the exact answer to the equation $7^{3x} = 60$ is found as follows:

$7^{3x} = 60$ begin with the given equation.

$log 7^{3x} = log 60$ take the log of both sides of the equation.

$3x log 7 = log 60$ apply the power property.

$x = \frac{log 60}{3 log 7}$ divide both sides of the equation by $3 log 7$.

using a calculator, evaluate the solution for $x$ to the nearest thousandth and then select the correct answer from the choices below.

$\bigcirc$ $x \approx 0.481$

$\bigcirc$ $x \approx 0.504$

$\bigcirc$ $x \approx 0.701$

$\bigcirc$ $x \approx 0.605$

Explanation:

Step1: Calculate \( \log 60 \)

Using a calculator, \( \log 60 \approx 1.77815125038 \)

Step2: Calculate \( \log 7 \)

Using a calculator, \( \log 7 \approx 0.84509804 \)

Step3: Calculate \( 3\log 7 \)

\( 3\log 7 = 3\times0.84509804 \approx 2.53529412 \)

Step4: Calculate \( \frac{\log 60}{3\log 7} \)

\( \frac{1.77815125038}{2.53529412} \approx 0.605 \)

Answer:

\( x \approx 0.605 \)