SOLUTION: please help me solve this problem using logarithms: {{{ 5(2^X) = 3 - 2^(x+2) }}}

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Question 434121: please help me solve this problem using logarithms: +5%282%5EX%29+=+3+-+2%5E%28x%2B2%29+
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
To solve the equation:5%2A2%5Ex=3-2%5E%28x%2B2%29, we substitute 2%5Ex=y and
2%5E%28x%2B2%29=2%5E2%2A2%5Ex=4%2Ay. Rewrite the equation: 5y=3-4y, solve this equation,
5y+4y=3 => 9y=3 => y=1/3. Now we find the x, since 2^x=y, substitute:
2%5Ex=1%2F3, taking natural logarithms of each side we have:
x%2Aln2=-ln3 => x=-ln3%2Fln2.
Done.