I have x/4 = lny This simplifies to y=e^(x-4)

Can someone help me understand the basic inverse properties of ln and e that would make x/(4 x ln)=y simplify to the answer above? Thanks.

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- Sep 17th 2011, 08:01 AMbenny92000Help simplifying basic expression with e
I have x/4 = lny This simplifies to y=e^(x-4)

Can someone help me understand the basic inverse properties of ln and e that would make x/(4 x ln)=y simplify to the answer above? Thanks. - Sep 17th 2011, 08:16 AMSironRe: Help simplifying basic expression with e
Use the definition of the logarithm: $\displaystyle \ln(x)=y \Leftrightarrow e^{y}=x$

- Sep 17th 2011, 08:18 AMTKHunnyRe: Help simplifying basic expression with e
I'm not sure "simplify" is the right word.

You should have this property...The following Two statements are identical.

1) $\displaystyle log_{b}(a) = c$

2) $\displaystyle b^{c} = a$

For suitable a, b, and c.

How does this apply to your problem statement?

Revise: See, SIRON even called it a "Definition". It's not really a "simplify" thing. - Sep 17th 2011, 08:29 AMbenny92000Re: Help simplifying basic expression with e
I understand the two statements and the conversion you guys give, but I don't know how to apply them correctly to this problem.

- Sep 17th 2011, 11:27 AMSironRe: Help simplifying basic expression with e
You can say: $\displaystyle \frac{x}{4}=\ln(y) \Leftrightarrow e^{\frac{x}{4}}=y$

- Sep 17th 2011, 11:59 AMe^(i*pi)Re: Help simplifying basic expression with e
- Sep 17th 2011, 12:44 PMbenny92000Re: Help simplifying basic expression with e
I don't remember the exact question. I understand it now. Thanks!