SOLUTION: Solve the equation 2^X=3^4-x. Write your solution exactly in terms of logarithms. Do not give a decimal approximation.

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Question 356163: Solve the equation 2^X=3^4-x. Write your solution exactly in terms of logarithms. Do not give a decimal approximation.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 2^X=3^4-x. Write your solution exactly in terms of logarithms. Do not give a decimal approximation.
2%5Ex%22%22=%22%223%5E%284-x%29
Take the log of both sides:
log%282%5Ex%29%22%22=%22%22log%283%5E%284-x%29%29
Move the exponents in front of the logs:
x%2Alog%282%29%22%22=%22%22%284-x%29log%283%29
Distribute on the right
x%2Alog%282%29%22%22=%22%224log%283%29-x%2Alog%283%29
Get the terms that contain x on the left and other one on the right:

x%2Alog%282%29%2Bx%2Alog%283%29%22%22=%22%224log%283%29
Factor out x on the left:
x%28log%282%29%2Blog%283%29%29%22%22=%22%224log%283%29
Divide both sides by %28log%282%29%2Blog%283%29%29
x%28log%282%29%2Blog%283%29%29%2F%28%28log%282%29%2Blog%283%29%29%29%22%22=%22%224log%283%29%2F%28%28log%282%29%2Blog%283%29%29%29
x%28cross%28log%282%29%2Blog%283%29%29%29%2F%28cross%28%28log%282%29%2Blog%283%29%29%29%29%22%22=%22%224log%283%29%2F%28log%282%29%2Blog%283%29%29
x%22%22=%22%224log%283%29%2F%28log%282%29%2Blog%283%29%29