simplify ln(ax^2)

Solution

simplify

ln (a x^{2})

ln (a) + 2 ln (x)

Solution steps

ln (a x^{2})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (a) + 2 ln (x)

ln (\frac{x ^{2} x ^{2} + 3}{( x + 3 ) ^{4}})

6 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

ln (v - 1) - ln (v)

ln (- \frac{1}{6} (x^{2} - 6 x + 5))

- lo g_{10} (4.4 \cdot 1 0^{- 4}) - 14