SOLUTION: Use logarithms to solve the equation 4^x=2(3^x), giving your answer correct to 3 significant figures.

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Question 865079: Use logarithms to solve the equation 4^x=2(3^x), giving your answer correct to 3 significant figures.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4%5Ex=2%283%5Ex%29 Start with the given equation.


ln%284%5Ex%29=ln%282%283%5Ex%29%29 Apply the natural log to both sides


ln%284%5Ex%29=ln%282%29%2Bln%283%5Ex%29 Using rule 1


x%2Aln%284%29=ln%282%29%2Bx%2Aln%283%29 Using rule 3


x%2Aln%284%29-x%2Aln%283%29=ln%282%29 Subtract x%2Aln%283%29 from both sides.


x%28ln%284%29-ln%283%29%29=ln%282%29 Factor out x


x%2Aln%284%2F3%29=ln%282%29 Using rule 2


x=ln%282%29%2Fln%284%2F3%29 Divide both sides by ln%284%2F3%29 to isolate x.


x=2.40942083965 Using a calculator here


x=2.41 Rounding to 3 significant figures