How do you use the Change of Base Formula and a calculator to evaluate the logarithm #log 32^8#?

1 Answer
Gió
Aug 11, 2015

I am not sure about the base of your log but try this:

Explanation:

Use the property of logs that says that:
#logx^a=alogx# and get:
#log(32)^8=8log(32)#
Now you can change base (the problem is: which is the base of your logarithm?).

Assuming base #10#, the change of base can obtained by using the formula:
#log_ab=ln(b)/ln(a)# where #ln# is the natural log that can be evaluated with a pocket calculator (actually in most calculators you can find also the log in base #10#!).
#8log(32)=8log_(10)(32)=8ln(32)/(ln10)=12.041#
If the original log was not in base #10# do not worry; substitute the given base #b# in:
#8log(32)=8log_(b)(32)=8ln(32)/(lnb)=# and evaluate it.

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