SOLUTION: log (base 3) x + log (base 5) 4x = 2

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Question 891810: log (base 3) x + log (base 5) 4x = 2
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39718) About Me  (Show Source):
You can put this solution on YOUR website!
You are starting with log%283%2Cx%29%2Blog%285%2C%284x%29%29=2
Use Change of Base into base 10.

log%2810%2Cx%29%2Flog%2810%2C3%29%2Blog%2810%2C%284x%29%29%2Flog%2810%2C5%29=2





log%2810%2Cx%5E0.69897%29%2Blog%2810%2C%284x%29%5E0.477121%29=0.666987

log%2810%2C%28x%5E0.69897%2A%284x%29%5E0.477121%29%29=0.666987,

log%2810%2C%284%5E0.477121%2Ax%5E%280.69897%2B0.477121%29%29%29=0.666987

log%2810%2C%284%5E%280.477121%29%2Ax%5E%281.176091%29%29%29=0.666987

log%2810%2C4%5E0.477121%29%2Blog%2810%2Cx%5E1.176091%29=0.666987

0.477121%2Alog%2810%2C4%29%2B1.176091%2Alog%2810%2Cx%29=0.666987

1.176091%2Alog%2810%2Cx%29=0.666987-0.477121%2Alog%2810%2C4%29



Can you finish from here?

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
log (base 3) x + log (base 5) 4x = 2

log+%283%2C+%28x%29%29+%2B+log+%285%2C+%284x%29%29+=+2

The way @JOSG did this problem, is not correct, in my opinion. This problem shouldn't be done with a calculator, especially
performing calculations from the beginning. As a matter of fact, I do believe that the answer should be EXACT.

I solved it and got the EXACT value of x to be: . This doesn't seem to coincide with his final answer.
You can do the CHECK!!