Find the solution of the exponential equation \( 15 e^{x}-10=2 \) in terms of logarithms, or correct to four decimal places. \( x=\square \) Question Help: Video

To solve the equation \( 15 e^{x} - 10 = 2 \), start by isolating \( e^{x} \): 1. Add 10 to both sides: \( 15 e^{x} = 12 \). 2. Divide by 15: \( e^{x} = \frac{12}{15} = \frac{4}{5} \). 3. Now, take the natural logarithm of both sides: \( x = \ln\left(\frac{4}{5}\right) \). Using a calculator, you can find that \( x \approx -0.2231 \) when rounded to four decimal places. So, the final result is: \( x \approx -0.2231 \).