What is xln(2)+5ln(x-1)-2ln(x+3) ?

The solution to xln(2)+5ln(x-1)-2ln(x+3) is xln(2)+ln(((x-1)^5)/((x+3)^2))

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simplify xln(2)+5ln(x-1)-2ln(x+3)

simplify

x ln (2) + 5 ln (x - 1) - 2 ln (x + 3)

x ln (2) + ln (\frac{( x - 1 ) ^{5}}{( x + 3 ) ^{2}})

Solution steps

x ln (2) + 5 ln (x - 1) - 2 ln (x + 3)

Apply log rule:

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

5 ln (x - 1) = ln ((x - 1)^{5})

= ln (2) x + ln ((x - 1)^{5}) - 2 ln (x + 3)

Apply log rule:

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

2 ln (x + 3) = ln ((x + 3)^{2})

= ln (2) x + ln ((x - 1)^{5}) - ln ((x + 3)^{2})

Apply log rule:

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

ln ((x - 1)^{5}) - ln ((x + 3)^{2}) = ln (\frac{( x - 1 ) ^{5}}{( x + 3 ) ^{2}})

= x ln (2) + ln (\frac{( x - 1 ) ^{5}}{( x + 3 ) ^{2}})

ln (\frac{243}{625})

ln (\frac{e ^{5}}{11})

\frac{1}{5} ln (2) + \frac{4}{5} ln (\frac{3}{4})

lo g_{3} (M) - lo g_{3} (N)

lo g_{5} (125) - lo g_{5} (\frac{5}{5})

What is xln(2)+5ln(x-1)-2ln(x+3) ?
The solution to xln(2)+5ln(x-1)-2ln(x+3) is xln(2)+ln(((x-1)^5)/((x+3)^2))