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)

Popular >

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)

2 lo g_{10} (3 x - 2) - lo g_{10} (2)

8 lo g_{b} (x) + 4 lo g_{b} (z)

3 ln (6 x) + ln (4 y)

2 ln (5) + 3 ln (2)

2 ln (6) - 2 ln (2)

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)