SOLUTION: can somebody help me solve this equation: {{{5^(x+2)=7^(x-2)}}}

Question 169002This question is from textbook college algebra
: can somebody help me solve this equation: This question is from textbook college algebra

Answer by Electrified_Levi(103) (Show Source): You can put this solution on YOUR website!
Hi, Hope I can help
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can somebody help me solve this equation:
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first we must take the log of both sides, log is the inverse function of an exponent, it is also the power of a base function
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The two sides will have a base of "10"
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, if there is an exponent in a log such as (x+2), and (x-2), you take the exponents and multiply them by (
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), in this case , and
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,
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We can rearrange the two sides
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=
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we can use the distribution to multiply the numbers out
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= =
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Remember the signs
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,
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now we need to get all the "x"s on one side, we will move , to the left side
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=
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=
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Now we will move to the right side
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=
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=
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We can take out the "x"s on the left side ( since they both have it in common
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=
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To find "x" you would divide both sides by
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= =
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=
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= (rounded)(you have to solve using a calculator)
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You usually check by replacing "x" with the answer, but in this case, it would be hard since the answer never stops ( I checked it, and it is right )
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Hope I helped, Levi
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