simplify 2ln(3x^2)

Solution

simplify

2 ln (3 x^{2})

2 ln (3) + 4 ln (x)

Solution steps

2 ln (3 x^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply the numbers:

2 \cdot 2 = 4

= 2 ln (3) + 4 ln (x)

ln (225) - 2 ln (3) + ln (e^{9})

ln (y) + 1 - ln (y + 1)

20 ln (x) - ln (x - 100)

lo g_{10} (X) + 2 lo g_{10} (y)

ln (5) + 2 ln (2)