# Thread: Is there a way to further reduce this?

1. ## Is there a way to further reduce this?

ln(y)=(2/3)*ln(x)

thanks

2. I am guessing that the text in the subject line is your question...?

What do you mean by "reducing" the equation?

3. ln(y)=(2/3)*ln(x)
= ln(y) = ln(x)^(2/3)
Multiplying both sides by e, we end up with:
y = x^(2/3)

4. thanks enjam, that's just what i was confused about. i didn't know that e^2/3lnx = x^2/3

5. Originally Posted by enjam
Multiplying both sides by e, we end up with:
y = x^(2/3)
Actually, no. If you multiply through by a constant, you will end up with the same logarithmic equation, but now multiplied through by a constant.

Instead, you need to raise both sides of the equation as powers on the base e.

Originally Posted by PandaNomium
i didn't know that e^2/3lnx = x^2/3
There's a good reason for not having know that: it's not true!

However, e^ln(x^(2/3)) does equal x^(2/3).

6. so what would be the simplified version of: e^(2/3lnx)

7. Originally Posted by PandaNomium
so what would be the simplified version of: e^(2/3lnx)
HI

e^[(2/3)lnx] would be x^(2/3)

8. property of logarithm: p(ln x) = ln (x)^p

ln(y)=(2/3)*ln(x) = ln (x)^(2/3)

raise BS to e,

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

but by definition, e^(ln y) = y, then

y = x^(2/3)

if you want a graph, see below.