How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log_3 40#?

1 Answer
MeneerNask
Jul 26, 2015

You divide #log(40)# by #log(3)# or divide #ln(40)# by #ln(3)#

Explanation:

Change of base means that you divide the log (to the new base) of the number by the log (to the new base) of the old base.

You may use #log=log_10# or the #ln=log_e# as long as you use the same button both times.

So:
#log_3 40=log40/log3=(1.6020...)/(0.4771...)=3.3577...#
Or:
#log_3 40=ln40/ln3=(3.6888...)/(1.0986...)=3.3577...#

Of course you can do this in one go, as long as you mind the brackets.

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