Question 15 If \( \ln (7 x+5)=2 \), then \( x= \)

To solve the equation \( \ln (7x + 5) = 2 \), we can exponentiate both sides to remove the natural logarithm. Thus, we have: \[ 7x + 5 = e^2 \] Next, we can isolate \( x \) by performing the following steps: 1. Subtract 5 from both sides: \[ 7x = e^2 - 5 \] 2. Finally, divide by 7: \[ x = \frac{e^2 - 5}{7} \] Now, let’s plug in the value of \( e^2\) (approximately 7.389) for a numerical approximation, resulting in: \[ x \approx \frac{7.389 - 5}{7} \approx \frac{2.389}{7} \approx 0.3413 \] So, the solution is \( x \approx 0.3413 \).