Asked by Lucille Nicole on May 06, 2024

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Solve the exponential equation. Round your answer to two decimal places. 7x+4=267 ^ { x + 4 } = 267x+4=26

A) x=-2.59
B) x=-2.33
C) x=-0.74
D) x=-3.40
E) x=4.60

Exponential Equation

An equation in which the variable appears in an exponent.

  • Address exponential equations and their application in various contexts.
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Verified Answer

ZK
Zybrea Knight

May 08, 2024

Final Answer :
B
Explanation :
Taking the logarithm of both sides with base 7 we get:
\begin{aligned} \log_7{(7^{x+4})} &= \log_7{26} \\ x+4 &= \log_7{26} \\ x &= \log_7{26}-4 \\ x &\approx -2.33 \end{aligned}
Therefore the answer is B, which is the only choice rounded to two decimal places.