What is 2ln(x^3*y^{12}) ?

The solution to 2ln(x^3*y^{12}) is 6ln(x)+24ln(y)

Popular >

simplify 2ln(x^3*y^{12})

simplify

2 ln (x^{3} \cdot y^{12})

6 ln (x) + 24 ln (y)

Solution steps

2 ln (x^{3} y^{12})

Apply log rule:

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

2 ln (x^{3} y^{12}) = 2 ln (x^{3}) + 2 ln (y^{12})

= 2 ln (x^{3}) + 2 ln (y^{12})

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 (y^{12})

Apply log rule:

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

ln (y^{12}) = 12 ln (y)

= 2 \cdot 3 ln (x) + 2 \cdot 12 ln (y)

Multiply the numbers:

2 \cdot 3 = 6

= 6 ln (x) + 2 \cdot 12 ln (y)

Multiply the numbers:

2 \cdot 12 = 24

= 6 ln (x) + 24 ln (y)

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

4 ln (x) - 3 ln (y) + 5 ln (z)

2 ln (5 x)

6 lo g_{10} (m) - 2 lo g_{10} (n)

- lo g_{10} (9.1 \cdot 1 0^{- 13})