What is expand ln((e^xe^2)^3) ?

The solution to expand ln((e^xe^2)^3) is 3x+6

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expand ln((e^xe^2)^3)

expand

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

3 x + 6

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 x ln (e) = 3 x

3 \cdot 2 ln (e) = 6

= 3 x + 6

\frac{1}{2} ln (ab)

lo g_{a} (\frac{x y ^{\frac{3}{5}}}{z ^{4}})

lo g_{4} (2) + 5 lo g_{4} (x)

3 lo g_{4} (a) + 3 lo g_{4} (b) - 3 lo g_{4} (c)