Asked by Briana Goins on May 07, 2024
Verified
Solve the exponential equation. Round your answer to two decimal places. 13(6x+4) =1200\frac { 1 } { 3 } \left( 6 ^ { x + 4 } \right) = 120031(6x+4) =1200
A) x=0.57x = 0.57x=0.57
B) x=−0.44x = - 0.44x=−0.44
C) x=7.87x = 7.87x=7.87
D) x=−0.66x = - 0.66x=−0.66
E) x=−2.68x = - 2.68x=−2.68
Exponential Equation
An equation in which the variable appears as an exponent.
Decimal Places
The number of digits to the right of the decimal point in a decimal number.
- Manage to solve exponential equations and apprehend their areas of application.
Verified Answer
JM
Jamiya MasonMay 13, 2024
Final Answer :
A
Explanation :
First, multiply both sides by 3 to get rid of the fraction: 6x+4=36006^{x+4} = 36006x+4=3600 . Taking the logarithm of both sides (base 6) gives x+4=log63600x + 4 = \log_6{3600}x+4=log63600 . Solving for xxx involves calculating the logarithm and subtracting 4. Using a calculator, log63600≈4.57\log_6{3600} \approx 4.57log63600≈4.57 , so x≈4.57−4=0.57x \approx 4.57 - 4 = 0.57x≈4.57−4=0.57 .
Learning Objectives
- Manage to solve exponential equations and apprehend their areas of application.