SOLUTION: Solve for x: 3^2x = 12 x = ? Round to 2 decimal places.

Question 70330: Solve for x: 3^2x = 12
x = ?
Round to 2 decimal places.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
I interpret your problem to be to solve for x in the equation:
.

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and I assume you know the use of logarithms and exponents.
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By using the power rule of exponents you can re-write the equation in the form:
.

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so substitute 9 for to reduce the equation to:
.

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Take the log of both sides to get:
.

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But by the rules of exponents in logarithms, the exponent becomes a multiplier of the
log. x is the exponent, so it becomes the multiplier of log(9) to give:
.

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To solve for x, divide both sides by log(9) to get:
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Calculator time! log(12) = 1.079181246 and log(9) = 0.954242509. By dividing log(12) by
log(9) you find that x = 1.130929754.
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That's the answer. By doubling it and raising 3 to that exponent on your calculator
you will find that the answer is, as it should be, 12.
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And don't forget to round the answer to two decimal places as the problem requests.
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Hope that I interpreted the problem correctly and that the approach I used was not beyond
where you are in your text.
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