Need help solving this logarithm

**mwok** · December 17th 2008, 02:47 AM

Write (equation) as the sum, difference, and/or constant multiple of logarithms.

Equation is attached.

**Moo** · December 17th 2008, 03:48 AM

Hello,

Originally Posted by mwok

Write (equation) as the sum, difference, and/or constant multiple of logarithms.

Equation is attached.

For any base of the logarithm, you have :
$\log_a (xy)=\log_a(x)+\log_a(y)$
$\log_a \left(\frac xy\right)=\log_a(x)-\log_a(y)$
$\log_a (x^y)=y \log_a(x)$

________________________________________________

Note that $\sqrt{z}=z^{1/2}$
$\log_5 \left(\frac{x^3}{y z^{1/2}}\right)=\log_5(x^3)-\log_5(yz^{1/2})=\dots$

Can you finish it ?

**mwok** · December 17th 2008, 04:32 AM

Thanks, attached is the solution I came up with (is it correct?).

BTW, does the solution answer all parts of the question (as the sum, difference, and/or constant multiple of logarithms?)

**Moo** · December 17th 2008, 05:20 AM

Originally Posted by mwok

Thanks, attached is the solution I came up with (is it correct?).

BTW, does the solution answer all parts of the question (as the sum, difference, and/or constant multiple of logarithms?)

Hey it's a z, not a 2 !

And it's not a sum and difference of logarithms...

Here is the thing :

$\log_5 \left(\frac{x^3}{y z^{1/2}}\right)=\log_5(x^3)-\log_5(yz^{1/2})$
$=3 \log_5(x) \quad - \quad \left(\log_5(y)+\log_5(z^{1/2})\right)$
$=3 \log_5(x)-\log_5(y)-\frac{\log_5(z)}{2}$

This is what you're asked to find. Do you understand the steps ? And what they mean by "sum, difference, and/or constant multiple of logarithms" ?

**mwok** · December 17th 2008, 05:34 AM

Thanks! Ah I see the solution and understand the steps.

But what do they mean by "sum, difference, and/or..."?

Does it mean just show the equation as a sum/difference of logarithms? Like in this case, we've shown a difference of logarithms?

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