What is 6ln(x+8)-9ln(x) ?

The solution to 6ln(x+8)-9ln(x) is ln(((x+8)^6)/(x^9))

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simplify 6ln(x+8)-9ln(x)

simplify

6 ln (x + 8) - 9 ln (x)

ln (\frac{( x + 8 ) ^{6}}{x ^{9}})

Solution steps

6 ln (x + 8) - 9 ln (x)

Apply log rule:

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

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

= ln ((x + 8)^{6}) - 9 ln (x)

Apply log rule:

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

9 ln (x) = ln (x^{9})

= ln ((x + 8)^{6}) - ln (x^{9})

Apply log rule:

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

ln ((x + 8)^{6}) - ln (x^{9}) = ln (\frac{( x + 8 ) ^{6}}{x ^{9}})

= ln (\frac{( x + 8 ) ^{6}}{x ^{9}})

\frac{5}{3} ln ∣ 5 ∣ - \frac{2}{3} ln ∣ 2 ∣

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5})

- 0.14 lo g_{2} (0.14) + (- 0.86) lo g_{2} (0.86)

ln (4 x e^{- 20 x})

10 lo g_{10} (\frac{( 2.5 \cdot 1 0 ^{- 3} )}{1000}) + 40 + 59

What is 6ln(x+8)-9ln(x) ?
The solution to 6ln(x+8)-9ln(x) is ln(((x+8)^6)/(x^9))