13. \( 5(7)^{5 x}=60 \)

To solve the equation \( 5(7)^{5x}=60 \), first, you can isolate the term with the exponent. Divide both sides by 5: \[ (7)^{5x} = \frac{60}{5} = 12 \] Next, you can take the natural logarithm of both sides, which allows you to bring down the exponent: \[ \ln((7)^{5x}) = \ln(12) \] This simplifies to: \[ 5x \cdot \ln(7) = \ln(12) \] Now, solve for \( x \): \[ x = \frac{\ln(12)}{5 \cdot \ln(7)} \] Substituting the approximate values of the logs: \[ x \approx \frac{2.4849}{5 \cdot 1.9459} \approx \frac{2.4849}{9.7295} \approx 0.255 \] So, the solution to the equation is \( x \approx 0.255 \).