What is 1/5 x^5(ln(3)+2ln(x)) ?

The solution to 1/5 x^5(ln(3)+2ln(x)) is (x^5ln(3x^2))/5

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simplify 1/5 x^5(ln(3)+2ln(x))

simplify

\frac{1}{5} x^{5} (ln (3) + 2 ln (x))

\frac{x ^{5} ln ( 3 x ^{2} )}{5}

Solution steps

\frac{1}{5} x^{5} (ln (3) + 2 ln (x))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= \frac{1}{5} x^{5} (ln (x^{2}) + ln (3))

Apply log rule:

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

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

= \frac{1}{5} x^{5} ln (3 x^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot x ^{5}}{5} ln (3 x^{2})

Multiply:

1 \cdot x^{5} = x^{5}

= \frac{x ^{5}}{5} ln (3 x^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{5} ln ( 3 x ^{2} )}{5}

ln (\frac{400}{250})

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

lo g_{e} (12) - lo g_{e} (6)

ln ((1 + e^{x})^{- e^{- x}} e^{\frac{1}{1 + e ^{x}}})

7 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y)

What is 1/5 x^5(ln(3)+2ln(x)) ?
The solution to 1/5 x^5(ln(3)+2ln(x)) is (x^5ln(3x^2))/5