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Solution:
Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.
Given that:
log4x - 1032 = 5
Apply anti-log on both sides
(4x - 10)5 = 32
(4x - 10)5 = 32
(4x - 10)5 = (2)5
If the exponents are equal, bases must be equal
4x - 10 = 2
4x = 12
x = 3
Summary:
The solution of log4x - 1032 = 5 is x = 3