Condense the logarithmic expression 1/2loga(w)+3loga(x)-loga(z)

 Esercizio

$\frac{1}{2}\log_a\left(w\right)+3\log_a\left(x\right)-\log_a\left(z\right)$

 

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

$\log_{a}\left(\sqrt{w}\right)+\log_{a}\left(x^3\right)-\log_{a}\left(z\right)$

 

Applicare la formula: $\log_{b}\left(x\right)-\log_{b}\left(y\right)$$=\log_{b}\left(\frac{x}{y}\right)$, dove $b=a$, $x=\sqrt{w}$ e $y=z$

$\log_{a}\left(\frac{\sqrt{w}}{z}\right)+\log_{a}\left(x^3\right)$

 

Applicare la formula: $\log_{a}\left(x\right)+\log_{a}\left(y\right)$$=\log_{a}\left(xy\right)$, dove $x=\frac{\sqrt{w}}{z}$ e $y=x^3$

$\log_{a}\left(\frac{\sqrt{w}}{z}x^3\right)$

 

Applicare la formula: $a\frac{b}{c}$$=\frac{ba}{c}$, dove $a=x^3$, $b=\sqrt{w}$ e $c=z$

$\log_{a}\left(\frac{\sqrt{w}x^3}{z}\right)$

$\log_{a}\left(\frac{\sqrt{w}x^3}{z}\right)$

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