SOLUTION: solve for x and round to nearest ten-thousandth 6^(3x) =60^(4x+5)

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Question 1071774: solve for x and round to nearest ten-thousandth
6^(3x) =60^(4x+5)
Found 2 solutions by josgarithmetic, MaxWong:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%286%5E%283x%29%29%29=log%28%2860%5E%284x%2B5%29%29%29

3x%2Alog%28%286%29%29=%284x%2B5%29%2Alog%28%2860%29%29
3x%2Alog%28%286%29%29=%284x%29%2Alog%28%2860%29%29%2B5%2Alog%28%2860%29%29
4x%2Alog%28%2860%29%29-3x%2Alog%28%286%29%29=-5%2Alog%28%2860%29%29
x%284%2Alog%28%2860%29%29-3%2Alog%28%286%29%29%29=-5%2Alog%28%2860%29%29

x=%28-5%2Alog%28%2860%29%29%29%2F%284%2Alog%28%2860%29%29-3%2Alog%28%286%29%29%29

choosing base 10,
x=%28-5%2A1.77815%29%2F%284%2A1.77815-3%2A0.77815%29
x=%28-8.89075%29%2F4.77815
x=-1.8607

Answer by MaxWong(38) About Me  (Show Source):
You can put this solution on YOUR website!
6%5E%283x%29=60%5E%284x%2B5%29
3x%2Aln%286%29+=+%284x%2B5%29%28ln%2860%29%29
3x%2Aln%286%29=%284x%2B5%29%28ln%286%29%2Bln%2810%29%29
3x%2Aln%286%29=4x%2Aln%286%29%2B5ln%286%29%2B4x%28ln%2810%29%29%2B5ln%2810%29
%284ln%2810%29-ln%286%29%29x=5ln%286%29%2B5ln%2810%29
x=%285ln%286%29%2B5ln%2810%29%29%2F%284ln%2810%29-ln%286%29%29
which is approximately 2.7595