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