Set 10: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Use logarithms to solve for $y$. 1. Given: $2^6 = 3^y$, so $64= 3^y$. 2. Take natural log: $\ln(64) = \ln(3^y) = y\ln(3)$. 3. Solve: $y = \frac{\ln(64)}{\ln(3)} = \frac{\ln(2^6)}{\ln(3)} = \frac{6\ln(2)}{\ln(3)}$. 4. Numerical: $y \approx \frac{6(0.693)}{1.099} \approx 3.79$. Strategic Tip: To solve $a^x = b$, use $x = \frac{\ln(b)}{\ln(a)}$. Choice B is incorrect because $3^6 = 729 \neq 64$. Choice C is incorrect because this inverts the logarithms. Choice D is incorrect because $3^4 = 81 \neq 64$.