Question

1. solve $4^{7x+5}=81.7$

Explanation:

Step1: Take log of both sides

$\log(4^{7x+5}) = \log(81.7)$

Step2: Apply log power rule

$(7x+5)\log(4) = \log(81.7)$

Step3: Isolate the linear term

$7x+5 = \frac{\log(81.7)}{\log(4)}$

Step4: Calculate the log ratio

$\frac{\log(81.7)}{\log(4)} \approx \frac{1.9122}{0.6021} \approx 3.176$

Step5: Solve for 7x

$7x = 3.176 - 5 = -1.824$

Step6: Solve for x

$x = \frac{-1.824}{7}$

Answer:

$x \approx -0.261$