Condense the logarithmic expression .5logm(x)+7logm(w)-logm(z)

 Esercizio

$.5\log_m\left(x\right)+7\log_m\left(w\right)-\log_m\left(z\right)$

 

Applicare la formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$

$\log_{m}\left(x^{0.5}\right)+\log_{m}\left(w^7\right)-\log_{m}\left(z\right)$

 

Applicare la formula: $\log_{b}\left(x\right)-\log_{b}\left(y\right)$$=\log_{b}\left(\frac{x}{y}\right)$, dove $b=m$, $x=x^{0.5}$ e $y=z$

$\log_{m}\left(\frac{x^{0.5}}{z}\right)+\log_{m}\left(w^7\right)$

 

Applicare la formula: $\log_{a}\left(x\right)+\log_{a}\left(y\right)$$=\log_{a}\left(xy\right)$, dove $a=m$, $x=\frac{x^{0.5}}{z}$ e $y=w^7$

$\log_{m}\left(\frac{x^{0.5}}{z}w^7\right)$

 

Applicare la formula: $a\frac{b}{c}$$=\frac{ba}{c}$, dove $a=w^7$, $b=x^{0.5}$ e $c=z$

$\log_{m}\left(\frac{x^{0.5}w^7}{z}\right)$

$\log_{m}\left(\frac{x^{0.5}w^7}{z}\right)$

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