Question 1084309: 1 + log3 5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1 + log3(5) is equivalent to 1 + log(5)/log(3)
you can use your calculator to see that the result is 2.464973521
the major concept used was:
loga(x) = logb(x)/logb(a)
this translates to log(x) to the base of a is equal to log(x) to the base of b divided by log(a)to the base of b.
that's the log base conversion formula that is widely used to convert any non-standard log base that can't be solved by the calculator to a base that can be used by the calculator.
those bases are the base of 10 which is the LOG function of the calculator, and the base of e which is the LN function of the calculator.
you can convert to either one and get the same answer.
example:
1 + log3(5) = 1 + log(5)/log(3) = 2.464973521
1 + log3(5) = 1 + ln(5)/ln(3) = 2.464973521
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