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Logarithm Equation

Question 1
If log1625 = xlog25 then x equals
Solution
Let y = log1625 = xlog25
when y = log1625
then 16y = 25
then (24)y = 52
then (2y)4 = 52 ...equation (1)
when y = xlog25
then y = log25x
then 2y = 5x ...equation (2)
Substitute the expression for 2y in equation (2) into equation (1)
(5x)4 = 52
then 54x = 52 then 4x = 2 then x = 1/2