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If (125)x = 3125 then the value of x is

This question belongs to Arithmetic Ability Algebra
Algebra
?

If (125)x = 3125, then the value of x is?

Answer & Solution
Correct Answer: Option C
$$\eqalign{ & {\left( {125} \right)^x} = 3125 \cr & \Rightarrow {\left( {{5^3}} \right)^x} = {\left( 5 \right)^5} \cr & \Rightarrow {\left( 5 \right)^{3x}} = {\left( 5 \right)^5} \cr & \Rightarrow 3x = 5 \cr & \Rightarrow x = \frac{5}{3} \cr} $$
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