simplify ln(k*x^n)

Solution

simplify

ln (k \cdot x^{n})

ln (k) + n ln (x)

Solution steps

ln (k x^{n})

Apply log rule:

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

ln (k x^{n}) = ln (k) + ln (x^{n})

= ln (k) + ln (x^{n})

Apply log rule:

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

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

= ln (k) + n ln (x)

f (x) = lo g_{10} (x^{4}) - lo g_{10} (x^{3})

- lo g_{b} (\frac{1}{2})

lo g_{3} (\frac{1}{10}) + lo g_{3} (50)

ln (\frac{( 0.132 \cdot 1 0 ^{- 3} ) ( 47 \cdot 1 0 ^{3} )}{10})