Questions: Solve the equation. 7 log (7 x)=28 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is □ (Type an exact answer. Use integers or fractions for any numbers in the expression.) B. There is no solution

Solution Steps

Starting with the equation: \[ 7 \log(7x) = 28 \] we divide both sides by 7 to isolate the logarithm: \[ \log(7x) = \frac{28}{7} = 4 \]

Next, we convert the logarithmic equation to its equivalent exponential form. The equation \(\log(7x) = 4\) can be rewritten as: \[ 7x = 10^4 \]

Now, we solve for \(x\) by dividing both sides by 7: \[ x = \frac{10^4}{7} = \frac{10000}{7} \approx 1428.5714 \]

Final Answer