SOLUTION: 1 task: http://f6.s.qip.ru/JIuHSX0O.jpg (picture) 2 task: http://f6.s.qip.ru/JIuHSX0N.jpg (picture) Please, could you help me to solve these tasks?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1 task: http://f6.s.qip.ru/JIuHSX0O.jpg (picture) 2 task: http://f6.s.qip.ru/JIuHSX0N.jpg (picture) Please, could you help me to solve these tasks?       Log On


   

Question 978888: 1 task: http://f6.s.qip.ru/JIuHSX0O.jpg (picture)
2 task: http://f6.s.qip.ru/JIuHSX0N.jpg (picture)
Please, could you help me to solve these tasks?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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1. First do a conversion of the equation.
Bring the linear term into the logarithm.
So then it looks like,
log%28%283%5Ex-6%29%2Csqrt%283%29%5E%286-2x%29%29%3C=1
Convert to log base 10,
log%2810%2C%28sqrt%283%29%5E%28%286-2x%29%29%29%29%2Flog%2810%2C%283%5Ex-6%29%29%3C=1
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From the graph you can see there are three regions of interest.
They are limited by the endpoints where,
3%5Ex-6=0
3%5Ex=6
x=ln%286%29%2Fln%283%29
.
.
3%5Ex-6=1
3%5Ex=7
x=ln%287%29%2Fln%283%29
So the function is less than 1 when,
highlight%28ln%286%29%2Fln%283%29%3Cx%3Cln%287%29%2Fln%283%29%29
.
.
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The other endpoint is determined when,
3%5Ex-6=3%5E%28x-3%29
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log%2810%2C%283%5E%28%283-x%29%29%29%29%2Flog%2810%2C%283%5Ex-6%29%29%3C=1
log%2810%2C%283%5E%28%283-x%29%29%29%29%3C=log%2810%2C%283%5Ex-6%29%29
3%5E%28%283-x%29%29%3C=3%5Ex-6
27%2A3%5E%28-x%29%3C=3%5Ex-6
27%3C=3%5E%282x%29-6%5E%28x%29
Which converts to a quadratic inequality,
y%5E2-6y-27%3E=0
%28y-9%29%28y%2B3%29%3E0
with solutions y%3E=9 and y%3C=-3
We can only use the positive solution.
y%3E=9
3%5Ex%3E=9
highlight%28x%3E=2%29
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The second problem is solved following the same procedure.