Asked by chrissstty friend on May 12, 2024
Verified
Solve the equation. Do not use a calculator. 4x+6=1164 ^ { x + 6 } = \frac { 1 } { 16 }4x+6=161
A) x=2x = 2x=2
B) x=8x = 8x=8
C) x=−51516x = - 5 \frac { 15 } { 16 }x=−51615
D) x=−8x = - 8x=−8
E) x=−512x = - 5 \frac { 1 } { 2 }x=−521
Equation
A mathematical formulation where two expressions are set equal to each other, indicating a balance.
- Work through exponential equations and gain an understanding of their use cases.
Verified Answer
MK
Moses Kabineh
May 16, 2024
Final Answer :
D
Explanation :
The equation can be solved by recognizing that 161616 is 424^242 and thus 116\frac{1}{16}161 is 4−24^{-2}4−2 . Setting the exponents equal to each other gives x+6=−2x + 6 = -2x+6=−2 , solving for xxx gives x=−8x = -8x=−8 .
Learning Objectives
- Work through exponential equations and gain an understanding of their use cases.