Quantitative Aptitude Ques 2148

Question: The value of x is $ 2^{3}(5^{0}+3^{2x})=8\frac{8}{27} $ is

Options:

A) $ \frac{3}{2} $

B) $ \frac{2}{3} $

C) $ -\frac{1}{3} $

D) $ \frac{-3}{2} $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ 2^{3}(5^{0}+3^{2x})=8\frac{8}{27} $
    $ \Rightarrow $ $ 8(1+3^{2x})=8+\frac{8}{27} $

$ \Rightarrow $ $ (1+3^{2x})=1+\frac{1}{27} $

$ \Rightarrow $ $ 3^{2x}=\frac{1}{27} $
$ \Rightarrow $ $ 3^{2x}={3^{-3}} $

$ \Rightarrow $ $ 2x=-3 $
$ \Rightarrow $ $ x=-3/2 $

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