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Tricky problem on solving a logarithmic system of equations
Problem 1
For given system of equations
exclude the parameter " a " and express x as a function of y.
Solution
You are given two equations (system of two equations)
= 5 (1)
= y (2)
Divide equation (1) by equation (2). You will get
= . (3)
Apply the change-of-base formula for logarithms to the left side of equation (3). Instead of equation (3), you will get then
= . (4)
It means that
x = y^(5/y). (5)
It is the sough expression of x via y, with parameter "a" excluded.
Expression (5) is your answer. It allows calculate the value of x for any given positive value of y.
