Solve each equation. 32^(x-1) = 16^(x/4) (The / is a division symbol not a fraction symbol) A.) 24 B.) 21 C.) -21 D.) 11

Question

Solve each equation.
`32^(x-1)` =
`16^(x/4)` (The / is a division symbol not a fraction symbol) A.) 24 B.) 21 C.) -21 D.) 11

Answer 1

x = 5/4

Explanation:

32^(x-1) = 16^(x/4)

(2^5)^(x-1) = (2^4)^(x/4) . . . . . express as powers of 2

2^(5x -5) = 2^x . . . . . . simplify

5x -5 = x . . . . . . equate exponents

4x = 5 . . . . . . . . add 5-x

x = 5/4

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Applicable rules of exponents are ...

(a^b)^c = a^(bc)

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Since this solution does not match any offered answer choice, we suggest you ask your teacher to show you how to work this problem.