SOLUTION: What is the value of X in this equation? log{{{7}}}X + log{{{7}}}X - log{{{7}}}3 = log{{{7}}}12
I was thinking that you could add log{{{7}}}3 to both sides of the equation. Howeve
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Question 20546: What is the value of X in this equation? logX + logX - log3 = log12
I was thinking that you could add log3 to both sides of the equation. However I don't know what to do next. Can you please help me out?
Answer by AnlytcPhil(1810) (Show Source): You can put this solution on YOUR website!
log7X + log7X = log712 + log73
`
The two terms on the left are just alike so when you add them you just get 2 of
them! That is, log7x + log7x = 2·log7x. So now you have
`
2·log7X = log712 + log73
`
Use the rule N·logBU = logBUN on the left
`
log7X2 = log712 + log73
`
Now use the rule logBU + logBV = logBUV
`
log7X2 = log7(12·3)
`
Now raise both sides to the 7 power, which is the same as dropping the logs.
`
X2 = 36
`
X = ±6, but we cannot take logs of negative numbers, so the answer is X = 6
`
Edwin
AnlytcPhil@aol.com
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