make x the subject of the equation y=3e^2x

write natural loarithm of x as ln(x)

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- Nov 20th 2008, 07:12 AM #1

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- Nov 20th 2008, 07:58 AM #2

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## Solving for x

If you want to solve for x, you should start by taking the natural log of both sides to get:

ln(y) = ln(3e^(2x))

ln(y) = ln(3) + ln(e^(2x)) Used this law: ln(XY) = ln(X) + ln(Y)

ln(y) = ln(3) + 2x*ln(e) Used this law: ln(X^y) = yln(X)

We know that ln(e) = 1, so equation can be rewritten:

ln(y) = ln(3) + 2x

ln(y) - ln(3) = 2x

ln(y/3) = 2x Used this law: ln(X/Y) = ln(X) - ln(Y)

Solve for x:

x = (1/2)*[ln(y/3)]

I consulted this website for the laws that were used to simplify the equation:

Exponents and Logarithms

Hope this helps