SOLUTION: I have a worksheet with several problems I need help with. I have the basic rules for logarithms, but they aren't really helping. 1. 5log(base37)37^9= 2. 3log(base24)24^-2/3

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Question 71483: I have a worksheet with several problems I need help with. I have the basic rules for logarithms, but they aren't really helping.
1. 5log(base37)37^9=
2. 3log(base24)24^-2/3=
3. (Log(base7)8)/(log(base7)1/8) =
4. 10^(log(base100)9)=
Thank you in advance for your help!!!
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Remember, "log of" simply means "exponent of".

1. 5log(base37)37^9=
log(base37) 37^(9*5)
=9*5 or 45
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2. 3log(base24)24^-2/3=
log(base 24) 24^(-2/3*3)
=log(base 24) 24^(-2)
= -2
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3. (Log(base7)8)/(log(base7)1/8) =
= log(base7)8 /[log(base7)1 - log(base7)8]
=log(base7)8 / -log(base7)8
= -1
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4. 10^(log(base100)9)=
10^[(log9)/log100]
=10^[(log9)/2]
=[10^log9]^(1/2)
=9^(1/2)
=3
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Cheers,
Stan H.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The best way to deal with logs is to think up a very simple
example that will show you how to do a problem, for instance,
What's ? Note that .
Say to yourself, What's the log to the base 2 that gives me
? You see that it's 4.
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(exactly like my example above)
answer
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answer
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Note the general rule that log(a/b) = log(a) - log(b) (with any base)
and also log(1) = 0 (with any base)

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