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Expert: - 5/24/2011


Question

equation
Find x in the equations in the image

Answer
(2x)^ln(2) = (3y)^ln(3) and 3^ln(x) = 2^ln(y).
Applying the ln() to each allows the exponent to be taken out front.
This gives ln(2)ln(2x) = ln(3)ln(3y) and ln(x)ln(3) = ln(y)ln(2).

Now it is known that ln(ab) = ln(a) + ln(b), so on the 1st equation we have
ln(2)[ln(2) + ln(x)] = ln(3)[ln(3) + ln(y)].

The 2nd equation can be used to say ln(x) = ln(y)ln(2)/ln(3).

This can be put in the 2nd equation that was just rewritten for ln(x),
then ln(y) can be solved for.

Once this is known, it can be put back in and ln(x) can be solved for.

Once both of these are known, the exponet of each side of both equations can be taken.
Doing so gives the value of x and the value of y.

Scott A Wilson

Expertise

Any algebraic question you've got, like linear, quadratic, exponential, etc.

Experience

solving story problems solving linear, parabolic, and 3rd order equations solving equations with multiple variables

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documents at Boeing

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MS at math OSU in mathematics at OSU BS at OSU in mathematical sciences (math, statistics, computer science)

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