Condense the logarithmic expression loge(a*b)+2loge(a*b^2)loge(a*b^3)

 Esercizio

$\log\:_e\left(ab\right)+2\log\:_e\left(ab^2\right)+\log\:_e\left(ab^3\right)$

 

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

$\log_{e}\left(abab^3\right)+2\log_{e}\left(ab^2\right)$

 

Applicare la formula: $x\cdot x^n$$=x^{\left(n+1\right)}$, dove $x^nx=abab^3$, $x=b$, $x^n=b^3$ e $n=3$

$\log_{e}\left(ab^{4}a\right)+2\log_{e}\left(ab^2\right)$

 

Applicare la formula: $x\cdot x$$=x^2$, dove $x=a$

$\log_{e}\left(a^2b^{4}\right)+2\log_{e}\left(ab^2\right)$

 

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

$\log_{e}\left(a^2b^{4}\right)+\log_{e}\left(\left(ab^2\right)^2\right)$

 

Applicare la formula: $\log_{a}\left(x\right)+\log_{a}\left(y\right)$$=\log_{a}\left(xy\right)$, dove $a=e$, $x=a^2b^{4}$ e $y=\left(ab^2\right)^2$

$\log_{e}\left(a^2b^{4}\left(ab^2\right)^2\right)$

$\log_{e}\left(a^2b^{4}\left(ab^2\right)^2\right)$

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