simplify ln(3(3)^2)

Solution

simplify

ln (3 (3)^{2})

3 ln (3)

Decimal Notation

3.29583 \dots

Solution steps

ln (3 (3)^{2})

Apply log rule:

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

ln (3 \cdot 3^{2}) = ln (3) + ln (3^{2})

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

Apply log rule:

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

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

= ln (3) + 2 ln (3)

Add similar elements:

ln (3) + 2 ln (3) = 3 ln (3)

= 3 ln (3)

ln (2 sin (2 x)) + cos (3 x)

ln (x^{3} (x + 8)^{5} (x^{2} + 8)^{5})

2 ln (2) - 2 ln (5)

ln (\frac{41}{66})

\frac{8 1 ^{l n (x)}}{4 ln ( 3 )} + C