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December 20, 2014

December 20, 2014

Posted by **john** on Monday, December 1, 2008 at 9:40pm.

log (base 9) x+3 log (base 3) x=14

- math -
**Damon**, Monday, December 1, 2008 at 9:57pmlog9(x) = log3(x) * log9(3)

what is log9(3)

9^log9(3) = 3

9^.5 = 3

so

log 9(x) = .5 log3(x)

Now the problem

.5 log3(x) + 3 log3(x) = 14

log3 (x^.5) + log3(x^3) = 14

log 3 (x^3.5) = 14

x^3.5 = 3^14

now use plain old base ten logs

3.5 log x = 14 log 3

log x = 1.91

x = 10^1.91 = 81.3

Check my arithmetic!!!

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