* 3_Chapter 3 (Course Work Question 55, 3.4.31 HW Scors: 60.60\%, 44.6 of CA ponts Pet 1 ol2 Pothtse 0 of 1 Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a catculator to obtain a decimal approximation for the solt \[ 7 e^{7 x}=1883 \] The solution set expressed in terms of logarithms is \( \square \) ]. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the equation. Use In for natural logarithm and log for common logarithm

Solve the equation \( 7e^{7x}=1883 \). Solve the equation by following steps: - step0: Solve for \(x\): \(7e^{7x}=1883\) - step1: Divide both sides: \(\frac{7e^{7x}}{7}=\frac{1883}{7}\) - step2: Divide the numbers: \(e^{7x}=269\) - step3: Take the logarithm of both sides: \(\ln{\left(e^{7x}\right)}=\ln{\left(269\right)}\) - step4: Evaluate the logarithm: \(7x=\ln{\left(269\right)}\) - step5: Divide both sides: \(\frac{7x}{7}=\frac{\ln{\left(269\right)}}{7}\) - step6: Divide the numbers: \(x=\frac{\ln{\left(269\right)}}{7}\) The solution set expressed in terms of natural logarithms is \( x = \frac{\ln{(269)}}{7} \). To obtain a decimal approximation for the solution, we can use a calculator. Using a calculator, we find that \( x \approx 0.799244 \).