SOLUTION: solve for x: log3^4-log3^x=2 no clue!!!

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Question 129545: solve for x:
log3^4-log3^x=2
no clue!!!
Found 3 solutions by stanbon, josmiceli, bimanewton:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log3^4-log3^x=2
log[3^4/3^x] = 2
log[3^(4-x)] = 2
(4-x)*log3 = 2
4-x = 2/log3
x = 4 - [2/log3]
x = -0.191806...
===================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%5E4%29+-+log%283%5Ex%29+=+2
Therre are a couple of general rules that help
log%28a%2Ab%29+=+log%28a%29+%2B+log%28b%29
and also
log%28a%2Fb%29+=+log%28a%29+-+log%28b%29
I can work this 2nd equation backwards
log%28a%29+-+log%28b%29+=+log%28a%2Fb%29
log%283%5E4%29+-+log%283%5Ex%29+=+log%28%283%5E4%29%2F%283%5Ex%29%29
log%28%283%5E4%29%2F%283%5Ex%29%29+=+2
I know that log%28100%29+=+2, so
log%28100%29+=+log%28%283%5E4%29%2F%283%5Ex%29%29
and it follows that
100+=+%283%5E4%29%2F%283%5Ex%29
100+=+81+%2F+3%5Ex
3%5Ex+=+.81
take the log of both sides
x%2Alog%283%29+=+log%28.81%29
x+=+log%28.81%29+%2F+log%283%29
x+=+-.1918
check answer
log%283%5E4%29+-+log%283%5Ex%29+=+2
log%2881%29+-+log%283%5E%28-.1918%29%29+=+2
1.9085+-+log%28.81%29+=+2
1.9085+-+%28-.0915%29+=+2
1.9085+%2B+.0915+=+2
2+=+2
OK

Answer by bimanewton(8) About Me  (Show Source):
You can put this solution on YOUR website!
change it into
log%28%283%5E4%29%2F%283%5Ex%29%29=log100
you can write and eliminated log
3%5E5%3E3%5E%284-x%29%3E3%5E4
then
5%3E4-x%3E4
x%3C0
x%3E-1
so
-1%3Cx%3C0