Log's - Please Help

**TheBigJ** · October 21st 2008, 12:15 PM

Hello, I have a question for you out their, please see attached file, i dont understand the question being asked off me, could someone explain it in plain english please.

Any help would be greatly appriciated.

Thanks

**Soroban** · October 21st 2008, 06:29 PM

Hello, TheBigJ!

Express the function $\frac{a^2b^3}{100\sqrt{x}}$ in terms of $\log_{10}(a),\;\log_{10}(b),\;\log_{10}(c)$

I'll omit the "subscript 10" . . .

Let $y \;=\;\frac{a^2b^3}{100\sqrt{c}}$

Take logs:

. . $\log(y) \;=\;\log\left(\frac{a^2b^3}{100\sqrt{c}}\right)$

. . $\log(y)\;=\;\log(a^2b^3) - \log(100\sqrt{c})$

. . $\log(y)\;= \;\log(a^2) + \log(b^3) - \bigg[\log(100) + \log(c^{\frac{1}{2}})\bigg]$

. . $\log(y) \;=\;\log(a^2) + \log(b^3) - \log(100) - \log(c^{\frac{1}{2}})$

. . $\log(y) \;=\;2\log(a) + 3\log(b) - 2 - \tfrac{1}{2}\log(c)$

Therefore: . $y \;=\;\frac{a^2b^3}{100\sqrt{c}} \;=\;10^{2\log(a) + 3\log(b) - 2 -\frac{1}{2}\log(c)}$

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