Question

solve for X(2/5)^2x-2=32/3125
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Answer 1

Given :

Expression given as : $(\frac{2}{5})^{2x-2}=\frac{32}{3125}$

To Find :

Value of x.

Solution:

$(\frac{2}{5})^{2x-2}=\frac{32}{3125}$

$(\frac{2}{5})^{2x-2}=\frac{2^5}{5^5}$

$(\frac{2}{5})^{2x-2}=(\frac{2}{5})^5$

By equating exponents of both the sides of the expression,

(2x - 2) = 5

2x = 5 + 2

x = $\frac{7}{2}$

x = 3.5