simplify ln(2x^7)

Solution

simplify

ln (2 x^{7})

ln (2) + 7 ln (x)

Solution steps

ln (2 x^{7})

Apply log rule:

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

ln (2 x^{7}) = ln (2) + ln (x^{7})

= ln (2) + ln (x^{7})

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= ln (2) + 7 ln (x)

2 lo g_{a} (3 x^{4}) - \frac{1}{2} lo g_{a} (3 x + 7)

2^{\frac{l n ( \frac{7}{4} )}{2 l n ( 2 )}}

lo g_{10} (K) + 3 lo g_{10} (L) - 5 lo g_{10} (T)

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 3}}{1})

3 lo g_{6} (x) - \frac{1}{5} lo g_{6} (y) + 2 lo g_{6} (w)