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 (\frac{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} (\frac{a}{b})

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

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

\frac{1}{- 0.06437} ln (\frac{1}{10})

ln (\frac{X - 3}{X + 3})

ln (I n x)

30 e^{9} + ln (\frac{12}{9}) + 40

4 lo g_{10} (0.1) - lo g_{10} (0.01)

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))