What is 8ln(x+6)-5ln(x) ?

The solution to 8ln(x+6)-5ln(x) is ln(((x+6)^8)/(x^5))

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simplify 8ln(x+6)-5ln(x)

simplify

8 ln (x + 6) - 5 ln (x)

ln (\frac{( x + 6 ) ^{8}}{x ^{5}})

Solution steps

8 ln (x + 6) - 5 ln (x)

Apply log rule:

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

8 ln (x + 6) = ln ((x + 6)^{8})

= ln ((x + 6)^{8}) - 5 ln (x)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln ((x + 6)^{8}) - ln (x^{5})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((x + 6)^{8}) - ln (x^{5}) = ln (\frac{( x + 6 ) ^{8}}{x ^{5}})

= ln (\frac{( x + 6 ) ^{8}}{x ^{5}})

- lo g_{10} (2.17 \cdot 1 0^{- 6})

5 ln (x) + ln (x^{2} + 7) - 9 ln (x + 7)

lo g_{10} (3.436 + 1) - lo g_{10} (1.718)

(0.717) ln (\frac{252}{17})

ln (\frac{2 x}{3}) + \frac{1}{8} ln (\frac{x}{4}) + \frac{3}{8} ln (\frac{3 x}{4})

What is 8ln(x+6)-5ln(x) ?
The solution to 8ln(x+6)-5ln(x) is ln(((x+6)^8)/(x^5))