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Solving for x using log/exponential laws

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Start by factorising both sides of the equation
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factor! 4^(x)-4^(x-1)=(4)4^(x-1)-(1)4^(x-1)=(3)4^(x-1)
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4\^x - 4\^(x-1) = 4\^x - (1/4)\*4\^x = (3/4)\*4\^x

3\^(x+1) - 3\^x = 3\*3\^x - 3\^x = 2\*3\^x

So, now you have:

(3/4)\*4\^x = 2\*3\^x

Now solve with logs. Note that log(8/3)=-log(3/8) and log(3/4)=-log(4/3), which migh come in handy depending on you proceed.

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