Why do you need to be careful when using the change of base rule of logarithms?
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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