Write (equation) as the sum, difference, and/or constant multiple of logarithms.
Equation is attached.
Hello,
For any base of the logarithm, you have :
$\displaystyle \log_a (xy)=\log_a(x)+\log_a(y)$
$\displaystyle \log_a \left(\frac xy\right)=\log_a(x)-\log_a(y)$
$\displaystyle \log_a (x^y)=y \log_a(x)$
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Note that $\displaystyle \sqrt{z}=z^{1/2}$
$\displaystyle \log_5 \left(\frac{x^3}{y z^{1/2}}\right)=\log_5(x^3)-\log_5(yz^{1/2})=\dots$
Can you finish it ?
Hey it's a z, not a 2 !
And it's not a sum and difference of logarithms...
Here is the thing :
$\displaystyle \log_5 \left(\frac{x^3}{y z^{1/2}}\right)=\log_5(x^3)-\log_5(yz^{1/2})$
$\displaystyle =3 \log_5(x) \quad - \quad \left(\log_5(y)+\log_5(z^{1/2})\right)$
$\displaystyle =3 \log_5(x)-\log_5(y)-\frac{\log_5(z)}{2}$
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" ?