Rewriting Equation

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August 30th 2009, 10:10 AM
WhoCares357

Rewriting Equation

I have to express the following two equations as a power of e.

a) $\pi^x$
b) x^(2x), x > 0

I don't necessarily need the answers. Rather an explanation or a link to an explanation would suffice.

Thank you.

Edit: The question was so simple that I overthought it. a) is just e^(-x*ln(pi))
August 30th 2009, 10:24 AM
Soroban

Hello, WhoCares357!

Quote:

Express the following functions as a power of $e.$

$a)\;\;y \:=\:\pi^x$

Take logs: . $\ln(y) \:=\:\ln(\pi^x) \quad\Rightarrow\quad \ln(y) \:=\:x\ln(\pi)$

Exponentiate: . $y \;=\;e^{x\ln(\pi)}$

Quote:

$b)\;\;y \:=\:x^{2x},\;\;x > 0$

Take logs: . $\ln(y) \;=\;\ln(x^{2x}) \quad\Rightarrow\quad \ln(y) \;=\;2x\ln(x)$

Exponentiate: . $y \;=\;e^{2x\ln(x)}$

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