SOLUTION: 3 exponent3x = 4 x 10 exponent x, find x 8 exponent3x/24=2730/2( exponent3x-2 ), find x

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Question 375800: 3 exponent3x = 4 x 10 exponent x, find x
8 exponent3x/24=2730/2( exponent3x-2 ), find x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the caret to signify an exponent. 3^(3x)=3%5E%283x%29
3%5E%283x%29=4%2A10%5E%28x%29
log%283%2C%283%5E%283x%29%29%29=log%283%2C%284%2A10%5E%28x%29%29%29
3x=log%283%2C%284%29%29%2Blog%283%2C%2810%5E%28x%29%29%29
3x=log%283%2C%284%29%29%2Bx%2Alog%283%2C%2810%29%29
3x-x%2Alog%283%2C%2810%29%29=log%283%2C%284%29%29
x%283-log%283%2C%2810%29%29%29=log%283%2C%284%29%29
highlight%28x=log%283%2C%284%29%29%2F%283-log%283%2C%2810%29%29%29%29
x=log%2810%2C%284%29%29%2F%283%2Alog%2810%2C3%29-log%2810%2C%2810%29%29%29
x=log%2810%2C%284%29%29%2F%283%2Alog%2810%2C3%29-1%29%29
or approximately,
x=1.3957