simplify ln(x^4y^3)

Solution

simplify

ln (x^{4} y^{3})

4 ln (x) + 3 ln (y)

Solution steps

ln (x^{4} y^{3})

Apply log rule:

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

ln (x^{4} y^{3}) = ln (x^{4}) + ln (y^{3})

= ln (x^{4}) + ln (y^{3})

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= 4 ln (x) + ln (y^{3})

Apply log rule:

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

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

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

(\frac{1}{0.143}) ln (\frac{5 x 1 0 ^{9}}{34000})

ln (\frac{1}{1 - c e ^{x}})

lo g_{a} (5) + 2 lo g_{a} (x) + 4 lo g_{a} (y^{3})

2 lo g_{10} (\frac{D v}{v} f) - 0.8

1 - 2 + ln (2) - ln (2)