What is 2ln(+x^3ln(x)) ?

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

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simplify 2ln(+x^3ln(x))

simplify

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

6 ln (x) + 2 ln (ln (x))

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply the numbers:

2 \cdot 3 = 6

= 6 ln (x) + 2 ln (ln (x))

ln (3 + 2 y) - ln (1 + 3 y)

2 ln (2) - 2 ln (3)

\frac{3 ln ( 2 )}{ln ( \frac{3}{2} )}

2 lo g_{10} (0.000001) + 2 lo g_{10} (0.001)

ln (\frac{1.61}{3.792})