SOLUTION: log 1- 6 logx = 9
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Question 894348: log 1- 6 logx = 9
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
log 1- 6 logx = 9
-----
log(1) = 0
-6log(x) = 9
log(x) = -1.5
x =~ 0.0316228
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
log(1) - 6log(x) = 9
you want to combine the logs into 1.
since 6log(x) = log(x^6), your equation becomes:
log(1) - log(x^6) = 9
since log(1) - log(x^6) = log(1/x^6), your equation becomes:
log(1/x^6) = 9
since log(1/x^6) = 9 if and only if 10^9 = 1/x^6, your equation becomes:
10^9 = 1/x^6
multiply both sides of this equation by x^6 to get:
10^9 * x^6 = 1
divide both sides of this equation by 10^9 to get:
x^6 = 1/10^9
take the 6th root of both sides of this equation to get:
x = (1/10^9)^(1/6)
solve for x using your calculator to get = .0316227766
let's see if this is a good solution.
your original equation is log(1) - 6*log(x) = 9
replace x with .0316227766 and you get:
log(1) - 6*log(.0316227766) = 9
simplify to get:
0 - 9 = 9 which results in 9 = 9 which confirms your solution is good.
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