Question

question 10 of 10
which of the following could be the first step in solving the equation below?
$4^x = 17$

a. $\log 4^x = 17$

b. $\log 4^x = \log 17$

c. $\sqrt4{4^x} = \sqrt4{17}$

d. $\frac{1}{4} \bullet 4^x = \frac{1}{4} \bullet 17$

Explanation:

Step1: Recall logarithm property

To solve \(4^x = 17\), we use the property that if \(a = b\), then \(\log a=\log b\) (taking logarithm on both sides).

Step2: Analyze each option

• Option A: Only taking log on left side, right side remains 17. Incorrect.
• Option B: Taking \(\log\) on both sides: \(\log 4^x=\log 17\). Correct first step.
• Option C: Taking 4th root is not standard first step for exponential equation with base 4 and constant 17. Incorrect.
• Option D: Multiplying by \(1/4\) doesn't help solve for \(x\) in exponential. Incorrect.

Answer:

B. \(\log4^x = \log17\)