How do you use the Change of Base Formula and a calculator to evaluate the logarithm log328?

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:
logxa=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:
logab=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)=8log10(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)=8logb(32)=8ln(32)lnb= and evaluate it.

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