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QuizMultiple Choice

Solving Exponential Equations by Rewriting the Base — Quiz

Question 3 • Mathematics III

Which equation is equivalent to 2 raised to the 4 x power is equal to 8 raised to the x minus 3 power ?

Answer
A
2 raised to the 4 x power is equal to 2 raised to the 2 x minus 6 power
B
2 raised to the 4 x power is equal to 2 raised to the 3 x minus 3 power
C
2 raised to the 4 x power is equal to 2 raised to the 3 x minus 9 power
D
2 raised to the 4 x power is equal to 2 raised to the 2 x minus 3 power

Explanation

Rewrite 8 as 2³. Then 8 raised to the x − 3 power is (2³)^(x − 3), which equals 2 raised to the 3x − 9 power by the power-of-a-power rule. So the equivalent equation is 2^(4x) = 2^(3x − 9), choice B.

AI-written and checked against the verified answer.

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