The change of base rule is one of the fundamental principles of logarithms. The change of base rule states that: log_a(b) = (log_c(b))/(log_c(a)) where c>1 (because the restriction on the base of a logarithm is that it must be greater than 1).
But even with this simple rule, we have to be very careful while solving equations.
Here is an example:
Here we are taking the changed base of the logarithm as 3. However when we look at the same question taken with a different base:
We get only 2 answers, not 3! The reason behind this uncanny discovery is that when we take the base of the logarithm as x, we are indirectly eliminating 1 as a valid solution for x. For this exact reason, always be careful when choosing a different base for the change of base rule.
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