What is ln(4)+2ln(x)+3ln(x^2+3) ?

The solution to ln(4)+2ln(x)+3ln(x^2+3) is ln(4x^2(x^2+3)^3)

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simplify ln(4)+2ln(x)+3ln(x^2+3)

simplify

ln (4) + 2 ln (x) + 3 ln (x^{2} + 3)

ln (4 x^{2} (x^{2} + 3)^{3})

Solution steps

ln (4) + 2 ln (x) + 3 ln (x^{2} + 3)

Apply log rule:

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

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

= ln (4) + ln (x^{2}) + 3 ln (x^{2} + 3)

Apply log rule:

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

ln (4) + ln (x^{2}) = ln (4 x^{2})

= ln (4 x^{2}) + 3 ln (x^{2} + 3)

Apply log rule:

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

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

= ln (4 x^{2}) + ln ((x^{2} + 3)^{3})

Apply log rule:

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

ln (4 x^{2}) + ln ((x^{2} + 3)^{3}) = ln (4 x^{2} (x^{2} + 3)^{3})

= ln (4 x^{2} (x^{2} + 3)^{3})

7 lo g_{3} (a) + 2 lo g_{3} (b) - \frac{1}{2} lo g_{3} (2 c)

lo g_{10} (a) - 2 lo g_{10} (b) + 3 lo g_{10} (c)

lo g_{10} (a) + 2 - 2 lo g_{10} (b)

4 lo g_{3} (x) + 7 lo g_{3} (y)

lo g_{2} (\frac{x ( x ^{2} + 1 )}{x ^{2} - 1})

What is ln(4)+2ln(x)+3ln(x^2+3) ?
The solution to ln(4)+2ln(x)+3ln(x^2+3) is ln(4x^2(x^2+3)^3)