Question 642127: i have been studying logarithms and i just cannot seem to understand them, so if someone would be so kind as to help me with this question and explain logarithms in the simplest way possible for me i would be very greatful.
Please note the "a" in this logarithm is subscript, not sure if that effects how to work it out or not.
Given logab = 3, use the properties of logarithms to evaluate
4loga1/b + 2logab^3
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! i have been studying logarithms and i just cannot seem to understand them, so if someone would be so kind as to help me with this question and explain logarithms in the simplest way possible for me i would be very greatful.
Please note the "a" in this logarithm is subscript, not sure if that effects how to work it out or not.
Given logab = 3, use the properties of logarithms to evaluate
4loga1/b + 2logab^3
**
In logs you must be able to identify 3 components:
The base
log of the number
the number
..
For given problem:
a is the common base for both terms
loga(b)=3 (given), reads: log of b, base a,=3
1/b is the number for the 1st term
b^3 is the number for the 2nd term
..
loga(1/b)=loga(b^-1)=-1loga(b)=-1*3=-3 (use exponent rule)
4loga(1/b)=4*-3=-12
..
loga(b^3)=3loga(b)=3*3=9 (use exponent rule)
2loga(b^3)=2*9=18
..
4loga(1/b) + 2loga(b^3)=-12+18=6
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