Asked by Lucille Nicole on May 06, 2024
Verified
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.
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.
\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.
Learning Objectives
- Address exponential equations and their application in various contexts.