What is ln(5)+2ln(x)+3ln(x^2+5) ?

The solution to ln(5)+2ln(x)+3ln(x^2+5) is ln(5x^2(x^2+5)^3)

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simplify ln(5)+2ln(x)+3ln(x^2+5)

simplify

ln (5) + 2 ln (x) + 3 ln (x^{2} + 5)

ln (5 x^{2} (x^{2} + 5)^{3})

Solution steps

ln (5) + 2 ln (x) + 3 ln (x^{2} + 5)

Apply log rule:

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

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

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

Apply log rule:

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

ln (5) + ln (x^{2}) = ln (5 x^{2})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{1}{9 ^{k}})

lo g_{3} (9 x y^{2}) - lo g_{3} (27 x y)

lo g_{10} (x y^{2})

ln (\frac{x}{x - 3}) + ln (\frac{x + 3}{x}) - ln (x^{2} - 9)

What is ln(5)+2ln(x)+3ln(x^2+5) ?
The solution to ln(5)+2ln(x)+3ln(x^2+5) is ln(5x^2(x^2+5)^3)