Question

due friday by 11:59pm points 100 submitting an external tool exam 3 100 points possible answered: 7/14 question 8 solve for x. round to three decimal places if needed. 6^x = 32 x = question help: message instructor next question

Explanation:

Step1: Take log on both sides

To solve \(6^x = 32\), we take the logarithm of both sides. Using the natural logarithm (ln) for convenience, we get \(\ln(6^x)=\ln(32)\).

Step2: Apply logarithm power rule

By the power rule of logarithms, \(\ln(a^b)=b\ln(a)\), so the left - hand side becomes \(x\ln(6)=\ln(32)\).

Step3: Solve for x

We can solve for \(x\) by dividing both sides by \(\ln(6)\): \(x = \frac{\ln(32)}{\ln(6)}\).
Now, we calculate the values: \(\ln(32)\approx3.4657\) and \(\ln(6)\approx1.7918\). Then \(x=\frac{3.4657}{1.7918}\approx1.934\).

Answer:

\(1.934\)