If \(9^{2x+5}=27^{3x-10},\) then \(x =\)
A. 3
B. 6
C. 8
D. 12
E. 15
Answer: C
Source: Magoosh
If \(9^{2x+5}=27^{3x-10},\) then \(x =\)
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Solution:Gmat_mission wrote: ↑Thu Oct 01, 2020 7:04 amIf \(9^{2x+5}=27^{3x-10},\) then \(x =\)
A. 3
B. 6
C. 8
D. 12
E. 15
Answer: C
We first must get a base of 3 for each expression so that we can then equate the exponents. Simplifying, we have:
(3^2)^(2x + 5) = (3^3)^(3x - 10)
3^(4x + 10) = 3^(9x - 30)
4x + 10 = 9x - 30
40 = 5x
8 = x
Answer: C
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