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Logarithm Equation

Question 1

If log₁₆25 = xlog₂5 then x equals

Solution

Let y = log₁₆25 = xlog₂5

when y = log₁₆25

then 16^y = 25

then (2⁴)^y = 5²

then (2^y)⁴ = 5² ...equation (1)

when y = xlog₂5

then y = log₂5^x

then 2^y = 5^x ...equation (2)

Substitute the expression for 2^y in equation (2) into equation (1)

(5^x)⁴ = 5²

then 5^4x = 5² then 4x = 2 then x = 1/2