Asked by Annette Corali on Mar 10, 2024
Verified
Solve the exponential equation. Round your answer to two decimal places. 7x=1197 ^ { x } = 1197x=119
A) x= 2.08
B) x= 4.78
C) x=2.46x = 2.46x=2.46
D) x=1.23x = 1.23x=1.23
E) x=2.83x = 2.83x=2.83
A) x= 2.08
B) x= 4.78
C) x=2.46x = 2.46x=2.46
D) x=1.23x = 1.23x=1.23
E) x=2.83x = 2.83x=2.83
Exponential Equation
An equation in which the variable appears in an exponent and involves exponential functions.
- Approach and understand the utility of exponential equations.
Verified Answer
MV
Marlene Vergara
Mar 10, 2024
Final Answer :
C
Explanation :
Take the logarithm of both sides of the equation:
7x=119ln(7x)=ln(119)xln(7)=ln(119)x=ln(119)ln(7)x=2.46…\begin{align*}7^x &= 119 \\\ln(7^x) &= \ln(119) \\x\ln(7) &= \ln(119) \\x &= \frac{\ln(119)}{\ln(7)} \\x &= 2.46\ldots \\\end{align*}7xln(7x)xln(7)xx=119=ln(119)=ln(119)=ln(7)ln(119)=2.46…
Rounding to two decimal places gives us $x=2.46$, which matches choice C.
7x=119ln(7x)=ln(119)xln(7)=ln(119)x=ln(119)ln(7)x=2.46…\begin{align*}7^x &= 119 \\\ln(7^x) &= \ln(119) \\x\ln(7) &= \ln(119) \\x &= \frac{\ln(119)}{\ln(7)} \\x &= 2.46\ldots \\\end{align*}7xln(7x)xln(7)xx=119=ln(119)=ln(119)=ln(7)ln(119)=2.46…
Rounding to two decimal places gives us $x=2.46$, which matches choice C.
Learning Objectives
- Approach and understand the utility of exponential equations.