QuestionJuly 16, 2025

Solve for x in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. 4^x+3=15 x= square

Solve for x in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. 4^x+3=15 x= square
Solve for x in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.
4^x+3=15
x= square

Solution
4.7(261 votes)

Answer

x \approx -0.54 Explanation 1. Take the logarithm of both sides Apply \log to both sides: \log(4^{x+3}) = \log(15). 2. Use the power rule for logarithms Simplify using **power rule**: (x+3) \cdot \log(4) = \log(15). 3. Solve for x Isolate x: x = \frac{\log(15)}{\log(4)} - 3.

Explanation

1. Take the logarithm of both sides<br /> Apply $\log$ to both sides: $\log(4^{x+3}) = \log(15)$.<br />2. Use the power rule for logarithms<br /> Simplify using **power rule**: $(x+3) \cdot \log(4) = \log(15)$.<br />3. Solve for x<br /> Isolate $x$: $x = \frac{\log(15)}{\log(4)} - 3$.
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