What is 3[ln(x)-2ln(x^2+1)]-2ln(5) ?

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

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simplify 3[ln(x)-2ln(x^2+1)]-2ln(5)

simplify

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

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

Solution steps

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

Apply log rule:

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

2 ln (x^{2} + 1) = ln ((x^{2} + 1)^{2})

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

Apply log rule:

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

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

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

Remove parentheses:

(a) = a

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

ln (\frac{x ^{2} y}{z ^{4}})

lo g_{5} (2 x - 5) + lo g_{5} (x - 3)

ln (21 e)

ln (\frac{2 x}{y ^{3}})

\frac{1}{2} ln (x) + 9 ln (y) - 8 ln (z)

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