simplify ln(100x^2)

Solution

simplify

ln (100 x^{2})

2 ln (10) + 2 ln (x)

Solution steps

ln (100 x^{2})

Apply log rule:

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

ln (100 x^{2}) = ln (100) + ln (x^{2})

= ln (100) + ln (x^{2})

Apply log rule:

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

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

= ln (100) + 2 ln (x)

ln (100) = 2 ln (10)

= 2 ln (10) + 2 ln (x)

lo g_{10} ((a + b) (a - b)^{2})

2 ln (x^{3} y \frac{1}{2})

lo g_{2} (49.92) - lo g_{2} (6.24)

ln (\frac{x}{e ^{7 x}})

\frac{19 ln ( \frac{8}{33} )}{9}