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# Logarithm Equation

- Question 1
- If log
_{16}25 = xlog_{2}5 then x equals

- Solution
- Let y = log
_{16}25 = xlog_{2}5 - when y = log
_{16}25 - then 16
^{y}= 25 - then (2
^{4})^{y}= 5^{2} - then (2
^{y})^{4}= 5^{2}...equation (1) - when y = xlog
_{2}5 - then y = log
_{2}5^{x} - then 2
^{y}= 5^{x}...equation (2) - Substitute the expression for 2
^{y}in equation (2) into equation (1) - (5
^{x})^{4}= 5^{2} - then 5
^{4x}= 5^{2}then 4x = 2 then x = 1/2