simplify ln(9x^2)

Solution

simplify

ln (9 x^{2})

2 ln (3) + 2 ln (x)

Solution steps

ln (9 x^{2})

Apply log rule:

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

ln (9 x^{2}) = ln (9) + ln (x^{2})

= ln (9) + ln (x^{2})

Apply log rule:

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

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

= ln (9) + 2 ln (x)

ln (9) = 2 ln (3)

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

ln (\frac{e ^{- (x - θ)}}{( 1 + e ^{- (x - θ)} ) ^{2}})

ln (\frac{e ^{\frac{9}{2}} 2 ( x )}{x ^{3}}) - ln ((y - 2)^{3} h (x))

\frac{1}{2} (lo g_{8} (s) + lo g_{8} (t))

lo g_{8} (x (x - 9))

lo g_{10} (x (x^{2} + 2)^{- \frac{1}{2}})