What is 2/7 ln|x+6|+5/7 ln|x-1| ?

The solution to 2/7 ln|x+6|+5/7 ln|x-1| is ln(|x+6|^{2/7}|x-1|^{5/7})

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simplify 2/7 ln|x+6|+5/7 ln|x-1|

simplify

\frac{2}{7} ln ∣ x + 6 ∣ + \frac{5}{7} ln ∣ x - 1 ∣

ln (∣ x + 6 ∣^{\frac{2}{7}} ∣ x - 1 ∣^{\frac{5}{7}})

Solution steps

\frac{2}{7} ln ∣ x + 6 ∣ + \frac{5}{7} ln ∣ x - 1 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{2}{7} ln ∣ x + 6 ∣ = ln (∣ x + 6 ∣^{\frac{2}{7}})

= ln (∣ x + 6 ∣^{\frac{2}{7}}) + \frac{5}{7} ln ∣ x - 1 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{5}{7} ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{\frac{5}{7}})

= ln (∣ x + 6 ∣^{\frac{2}{7}}) + ln (∣ x - 1 ∣^{\frac{5}{7}})

Apply log rule:

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

ln (∣ x + 6 ∣^{\frac{2}{7}}) + ln (∣ x - 1 ∣^{\frac{5}{7}}) = ln (∣ x + 6 ∣^{\frac{2}{7}} ∣ x - 1 ∣^{\frac{5}{7}})

= ln (∣ x + 6 ∣^{\frac{2}{7}} ∣ x - 1 ∣^{\frac{5}{7}})

- lo g_{10} (0.6 (1 0^{- 3}))

ln (12 \frac{12}{5})

10 lo g_{10} (56.27) - 10 lo g_{10} (33.52)

ln (\frac{11}{0.5})

\frac{1}{16} ln (\frac{18}{10})

What is 2/7 ln|x+6|+5/7 ln|x-1| ?
The solution to 2/7 ln|x+6|+5/7 ln|x-1| is ln(|x+6|^{2/7}|x-1|^{5/7})