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.