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Find the value of x that satisfies the equation $$25^{-2}= \frac{5^{48/x}}{5^{26/x}\cdot 25^{17/x}}$$

Feb 26, 2019

#1
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Solve for x:
1/625 = 5^(-12/x)

1/625 = 5^(-12/x) is equivalent to 5^(-12/x) = 1/625:
5^(-12/x) = 1/625

Take reciprocals of both sides:
5^(12/x) = 625

Take the logarithm base 5 of both sides:
12/x = 4

Take the reciprocal of both sides:
x/12 = 1/4

Multiply both sides by 12:

x = 3

Feb 26, 2019
edited by Guest  Feb 26, 2019

#1
+1

Solve for x:
1/625 = 5^(-12/x)

1/625 = 5^(-12/x) is equivalent to 5^(-12/x) = 1/625:
5^(-12/x) = 1/625

Take reciprocals of both sides:
5^(12/x) = 625

Take the logarithm base 5 of both sides:
12/x = 4

Take the reciprocal of both sides:
x/12 = 1/4

Multiply both sides by 12:

x = 3

Guest Feb 26, 2019
edited by Guest  Feb 26, 2019