Asked by Rishi Gowda on May 11, 2024
Verified
Solve the exponential equation. Round your answer to two decimal places. 4+e2−x=204 + e ^ { 2 - x } = 204+e2−x=20
A) x=−0.77x = - 0.77x=−0.77
B) x=5.18x = 5.18x=5.18
C) x=0.80x = 0.80x=0.80
D) x=4.77x = 4.77x=4.77
E) x=−0.39x = - 0.39x=−0.39
Exponential Equation
An exponential equation is one in which the variable appears in the exponent, for example, \(2^x = 8\).
Decimal Places
In a numerical value, decimal places denote the quantity of digits after the decimal point, such as two decimal places in 12.34.
- Address and grasp the practical implications of exponential equations.
Verified Answer
PP
Peter Phung
May 16, 2024
Final Answer :
A
Explanation :
First, isolate the exponential term: e2−x=16e^{2-x} = 16e2−x=16 . Taking the natural logarithm of both sides gives 2−x=ln(16)2-x = \ln(16)2−x=ln(16) . Solving for xxx yields x=2−ln(16)x = 2 - \ln(16)x=2−ln(16) , which approximately equals −0.77-0.77−0.77 .
Learning Objectives
- Address and grasp the practical implications of exponential equations.