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Question 64483: I don't even know where to start with this one, looking for help
Solve for x
27.) log x = (2/3) log 8 – (2 log 5 + log 2)
28.) log (x – 1) + log (x – 1) = log 3
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 27.) log x = (2/3) log 8 – (2 log 5 + log 2)
:
You don't even need to find the logs of these, use the exponent equiv & rules:
log x = log(8^(2/3)) - log(5^2) + log (2)
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you know that Cube root of 8 is 2, and 2^2 = 4, 5^2 is 25, so you have:
log x = log(4) - (log(25) + log(2))
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Adding logs is that same as multiply so you have:
log x = log(4) - log(50)
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Subtracting logs is the same as dividing so you have:
log x = log(4/50)
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if the log of x = log (4/50) then
x = 4/50
x = .08
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28.) log (x – 1) + log (x – 1) = log 3
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You are adding like terms so you have:
2*log(x-1) = log 3
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Find the log of 3
2*log(x-1) = .477
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Divide both sids by 2:
log(x-1) = .477/2
log(x-1) = .2385
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Find the anti log (10^) of both sides:
x - 1 = 1.732
x = 1.732 + 1
x = 2.732
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Check using a calc:
2*log(1.732) = log(3)
2 * .2385 = .477
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