Need help simplifying an equation

**alexpollema** · April 5th 2011, 07:43 PM

I am attempting my economics homework and have an answer but I am not sure if I have it simplified as far as possible. I need a little help brushing up on my log rules. Please let me know if I can simplify this answer further:

e^[15-.5ln(w)]

I believe it can be simplified further like this:

e^15-e^.5ln(w) = e^15-w*e^.5

Is this correct? If not can you please give me the correct log and e rules to simplify this correctly?

**pickslides** · April 5th 2011, 07:51 PM

$\displaystyle a^{m-n} = a^m \div a^n$

**TheChaz** · April 5th 2011, 07:53 PM

$e^{15 - .5ln(w)} = \frac{e^{15}}{e^{.5ln(w)}}$
.
$\frac{e^{15}}{e^{ln(w^{.5})}} = \frac{e^{15}}{\sqrt(w)}$

**alexpollema** · April 5th 2011, 08:04 PM

Thank you.

So then is this simplification correct:

e^.5ln(w)=w*e^.5

**Prove It** · April 5th 2011, 08:06 PM

No. First simplify the logarithm, then get rid of it using the exponential.

**alexpollema** · April 5th 2011, 08:07 PM

i see it now. Thank you to all who contributed

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