c. \( 0.405=15.6(0.72)^{x} \)

To solve the equation \( 0.405 = 15.6(0.72)^{x} \), start by isolating the exponential term. Divide both sides by 15.6 to get: \[ (0.72)^{x} = \frac{0.405}{15.6} \] Calculating the right side gives approximately \( 0.02596 \). Now, take the logarithm of both sides – you can use either natural logarithm \( \ln \) or common logarithm \( \log \): \[ \ln((0.72)^{x}) = \ln(0.02596) \] Using the power property of logarithms, bring down \( x \): \[ x \cdot \ln(0.72) = \ln(0.02596) \] Finally, solve for \( x \) by dividing both sides by \( \ln(0.72) \): \[ x = \frac{\ln(0.02596)}{\ln(0.72)} \] With this calculation, you can find the approximate value of \( x \). Using a calculator will show that \( x \) is around 6.5! So, you found \( x \) where the numbers add up to thrilling proportions in your mathematical adventure!