What is 4ln(x-5)+5/4 ln(x+1)-3ln(x) ?

The solution to 4ln(x-5)+5/4 ln(x+1)-3ln(x) is ln(((x-5)^4(x+1)^{5/4})/(x^3))

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simplify 4ln(x-5)+5/4 ln(x+1)-3ln(x)

simplify

4 ln (x - 5) + \frac{5}{4} ln (x + 1) - 3 ln (x)

ln (\frac{( x - 5 ) ^{4} ( x + 1 ) ^{\frac{5}{4}}}{x ^{3}})

Solution steps

4 ln (x - 5) + \frac{5}{4} ln (x + 1) - 3 ln (x)

Apply log rule:

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

4 ln (x - 5) = ln ((x - 5)^{4})

= ln ((x - 5)^{4}) + \frac{5}{4} ln (x + 1) - 3 ln (x)

Apply log rule:

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

\frac{5}{4} ln (x + 1) = ln ((x + 1)^{\frac{5}{4}})

= ln ((x - 5)^{4}) + ln ((x + 1)^{\frac{5}{4}}) - 3 ln (x)

Apply log rule:

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

ln ((x - 5)^{4}) + ln ((x + 1)^{\frac{5}{4}}) = ln ((x - 5)^{4} (x + 1)^{\frac{5}{4}})

= ln ((x - 5)^{4} (x + 1)^{\frac{5}{4}}) - 3 ln (x)

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln ((x - 5)^{4} (x + 1)^{\frac{5}{4}}) - ln (x^{3})

Apply log rule:

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

ln ((x - 5)^{4} (x + 1)^{\frac{5}{4}}) - ln (x^{3}) = ln (\frac{( x - 5 ) ^{4} ( x + 1 ) ^{\frac{5}{4}}}{x ^{3}})

= ln (\frac{( x - 5 ) ^{4} ( x + 1 ) ^{\frac{5}{4}}}{x ^{3}})

lo g_{4} (\frac{64}{x + 7})

3 lo g_{6} (u) + 5 lo g_{6} (v)

ln (\frac{- 1}{1})

lo g_{10} (4) + lo g_{10} (x)

What is 4ln(x-5)+5/4 ln(x+1)-3ln(x) ?
The solution to 4ln(x-5)+5/4 ln(x+1)-3ln(x) is ln(((x-5)^4(x+1)^{5/4})/(x^3))