help with this please

**rj2001** · December 5th 2008, 01:42 PM

not sure what to do

**Soroban** · December 5th 2008, 02:21 PM

Hello, rj2001!

Sove for $x\!:\;\;\pi^{1-4x} \:=\:e^{5x}$

Take logs: . $\ln\left(\pi^{1-4x}\right) \;=\;\ln\left(e^{5x}\right) \quad\Rightarrow\quad(1-4x)\ln(\pi) \;=\;5x\ln(e)$

Since $\ln(e) = 1$ , we have: . $\ln(\pi) - 4x\ln(\pi) \;=\;5x \quad\Rightarrow\quad 4x\ln(\pi) + 5x \;=\;\ln(\pi)$

Factor: . $x\bigg[4\ln(\pi) + 5\bigg] \;=\;\ln(\pi)$

Therefore: . $x \;=\;\frac{\ln(\pi)}{4\ln(\pi) + 5}$

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help with this please