What is the base conversion formula for logarithms?

1 Answer
AJ Speller
Oct 4, 2014

Log base "a" of "x" is the same quotient of log base"b" of "x" and log base "b" of "a".

This allows us to convert a base that is not easily solvable into the division of of logs with common base that is easy to solve.

#log_a(x)=(log_b(x))/(log_b(a))#

#log_10(100)=(log_e(100))/(log_e(10))=(ln(100))/(ln(10))=2#

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