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.

Related questions
See all questions in Functions with Base b
Impact of this question
2521 views around the world
You can reuse this answer
Creative Commons License