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

Question 129545: solve for x:
log3^4-log3^x=2
no clue!!!
Found 3 solutions by stanbon, josmiceli, bimanewton:
Answer by stanbon(75887)   (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)   (Show Source): You can put this solution on YOUR website!

Therre are a couple of general rules that help

and also

I can work this 2nd equation backwards

I know that , so

and it follows that

take the log of both sides

check answer

OK

Answer by bimanewton(8)   (Show Source): You can put this solution on YOUR website!
change it into

you can write and eliminated log

then

so

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