Question

what is the solution to the equation $2^{5x}=6$? enter the answer to the nearest hundredth.

Explanation:

Step1: Take log of both sides

$\log(2^{5x}) = \log(6)$

Step2: Apply log power rule

$5x\log(2) = \log(6)$

Step3: Isolate x term

$5x = \frac{\log(6)}{\log(2)}$

Step4: Solve for x

$x = \frac{\log(6)}{5\log(2)}$

Step5: Calculate and round

$x = \frac{0.7782}{5\times0.3010} \approx \frac{0.7782}{1.505} \approx 0.52$

Answer:

0.52