SOLUTION: Use algebraic procedures to find the exact solution(s) of the equation. log(6x-21)=2+log(x-9) I am taking an online class so I have to learn this stuff by myself pretty much. I

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Use algebraic procedures to find the exact solution(s) of the equation. log(6x-21)=2+log(x-9) I am taking an online class so I have to learn this stuff by myself pretty much. I       Log On


   

Question 923954: Use algebraic procedures to find the exact solution(s) of the equation.
log(6x-21)=2+log(x-9)
I am taking an online class so I have to learn this stuff by myself pretty much. I have looked everywhere for how to do this problem and I can't find anything. I would really appreciate a step-by-step answer.Thank you!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use algebraic procedures to find the exact solution(s) of the equation.
log(6x-21)=2+log(x-9)
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You need to know:: log(A)-log(B) = log(A/B)
and
logx(3) 2 implies that 3 = x^2
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Your problem::
log(6x-21) - log(x-3) = 2
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log[(6x-21)/(x-3)] = 2
----
(6x-21)/(x-3) = 10^2
-------
6x-21 = 100x - 300
94x = 279
x = 2.9681
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%286x-21%29%29=2%2Blog%28%28x-9%29%29


log%28%286x-21%29%29-log%28%28x-9%29%29=2


log%28%28%286x-21%29%2F%28x-9%29%29%29=2 Use log rule #2 from this page


%286x-21%29%2F%28x-9%29=10%5E2


%286x-21%29%2F%28x-9%29=100 Convert to exponential form (logs without stated bases are by default in base 10)


6x-21=100%28x-9%29


6x-21=100x-900


6x-21%2B900=100x


-21%2B900=100x-6x


879=94x


94x=879


x=879%2F94

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Answer:

The exact answer is x=879%2F94

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Let me know if that helps or not. Thanks.

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