Write th folowing in Logarithmic Form

**jp.101** · Dec 17th 2008, 04:03 AM

I am really stuck with this problem, any help would be greatly appreciated

d^5/f^2=h^0.25(c/e-g)^3

Thanks,

JP

**Soroban** · Dec 17th 2008, 08:29 AM

Hello, JP!

The instructions are rather vague.

I assume we are to take logs ... then "expand" the expression.

$\frac{d^5}{f^2} \:=\:h^{\frac{1}{4}}\left(\frac{c}{e-g}\right)^3$

We have: . $\log\left(\frac{d^5}{f^2}\right) \;=\;\log\left[h^{\frac{1}{4}}\left(\frac{c}{e-g}\right)^3\right]$

. . . $\log(d^5) - \log(f^2) \;=\;\log\left(h^{\frac{1}{4}}\right) + \log\left(\frac{c}{e-g}\right)^3$

. . . $5\log(d) - 2\log(f) \;=\;\frac{1}{4}\log(h) + 3\log\left(\frac{c}{e-g}\right)$

. . . $5\log(d) - 2\log(f) \;=\;\tfrac{1}{4}\log(h) + 3\bigg[\log(c) - \log(e-g)\bigg]$

. . . $5\log(d) - 2\log(f) \;=\;\tfrac{1}{4}\log(h) + 3\log(c) - 3\log(e-g)$

**jp.101** · Dec 17th 2008, 09:21 AM

thanks very much on that one

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