What is expand ln((e^zx^2y)^3) ?

The solution to expand ln((e^zx^2y)^3) is 3z+6ln(x)+3ln(y)

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expand ln((e^zx^2y)^3)

expand

ln ((e^{z} x^{2} y)^{3})

3 z + 6 ln (x) + 3 ln (y)

Solution steps

ln ((e^{z} x^{2} y)^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((e^{z} x^{2} y)^{3}) = 3 ln (e^{z} x^{2} y)

= 3 ln (e^{z} x^{2} y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

3 ln (e^{z} x^{2} y) = 3 ln (e^{z}) + 3 ln (x^{2}) + 3 ln (y)

= 3 ln (e^{z}) + 3 ln (x^{2}) + 3 ln (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{z}) = z ln (e)

= 3 z ln (e) + 3 ln (x^{2}) + 3 ln (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= 3 z ln (e) + 3 \cdot 2 ln (x) + 3 ln (y)

3 z ln (e) = 3 z

3 \cdot 2 ln (x) = 6 ln (x)

= 3 z + 6 ln (x) + 3 ln (y)

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What is expand ln((e^zx^2y)^3) ?
The solution to expand ln((e^zx^2y)^3) is 3z+6ln(x)+3ln(y)