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Write the expression as a sum, difference, or product of logarithms

Attachment 23309

I am in need of help please...I have no idea where to begin on this one...could somebody take me through the process please?

Re: Write the expression as a sum, difference, or product of logarithms

log baseb (4x^9/z^8)^1/2 = logb 2x^3/z^4 = log 2 +3logx -4logz (all logs base b)

Re: Write the expression as a sum, difference, or product of logarithms

Quote:

Originally Posted by

**aikenfan** Attachment 23309
I am in need of help please...I have no idea where to begin on this one...could somebody take me through the process please?

$\displaystyle \log_{b}\sqrt {\frac{4x^9}{z^8}}=\frac{1}{2} \cdot \log_{b} \frac{4x^9}{z^8}=\frac{1}{2} \cdot(\log_{b}4x^9-\log_{b}z^8)=$

$\displaystyle =\frac{1}{2} \cdot (\log_{b} 4+9\log_{b} x-8 \log_{b}z)$

Re: Write the expression as a sum, difference, or product of logarithms

[QUOTE=princeps;708543]$\displaystyle \log_{b}\sqrt {\frac{4x^9}{z^8}}=\frac{1}{2} \cdot \log_{b} \frac{4x^9}{z^8}=\frac{1}{2} \cdot(\log_{b}4x^9-\log_{b}z^8)=$

$\displaystyle =\frac{1}{2} \cdot (\log_{b} 4+9\log_{b} x-8 \log_{b}z)$[/QUOTE

Thanks for correcting my mistake