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3(2)^X=9
 Feb 10, 2014
 #1
avatar+6251 
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Quote:

3(2)^X=9



3*2 X = 9 ; divide both sides by 3

2 X = 3 ; take the log base 2 of both sides

LOG 2(2 X) = LOG 2(3) ; use definition of logarithm of a base

X = LOG 2(3)
 Feb 10, 2014
 #2
avatar+118654 
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Rom:
Quote:

3(2)^X=9



3*2 X = 9 ; divide both sides by 3

2 X = 3 ; take the log base 2 of both sides

LOG 2(2 X) = LOG 2(3) ; use definition of logarithm of a base

X = LOG 2(3)



Rom's answer is really good.
I just want to add a little

2 X = 3
You can just take the log of both sides using any base. You calc deals with base 10 and base e so I'd choose one of those.
log 2 X = log 3
X*log 2 = log 3

x = log3 / log2
and then you can estimate it from your calc.

NOTE
Rom's answer was X = LOG 2(3)[/quote]
Using change of base rule these two answers are identical.
you might like to keep this reference page close by
http://en.wikipedia.org/wiki/List_of_logarithmic_identities
 Feb 11, 2014

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