What is ln(4)+3ln(x)+5ln(x^2+10) ?

The solution to ln(4)+3ln(x)+5ln(x^2+10) is ln(4x^3(x^2+10)^5)

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simplify ln(4)+3ln(x)+5ln(x^2+10)

simplify

ln (4) + 3 ln (x) + 5 ln (x^{2} + 10)

ln (4 x^{3} (x^{2} + 10)^{5})

Solution steps

ln (4) + 3 ln (x) + 5 ln (x^{2} + 10)

Apply log rule:

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

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

= ln (4) + ln (x^{3}) + 5 ln (x^{2} + 10)

Apply log rule:

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

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

= ln (4 x^{3}) + 5 ln (x^{2} + 10)

Apply log rule:

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

5 ln (x^{2} + 10) = ln ((x^{2} + 10)^{5})

= ln (4 x^{3}) + ln ((x^{2} + 10)^{5})

Apply log rule:

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

ln (4 x^{3}) + ln ((x^{2} + 10)^{5}) = ln (4 x^{3} (x^{2} + 10)^{5})

= ln (4 x^{3} (x^{2} + 10)^{5})

ln (6) - 3 ln (a) + ln (b)

u^{2} + 2 u - 4 ln (u) + 2 ln (y)

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

ln (x + 1) + ln (k)

ln (X) + ln (Y) - 3 ln (Z)

What is ln(4)+3ln(x)+5ln(x^2+10) ?
The solution to ln(4)+3ln(x)+5ln(x^2+10) is ln(4x^3(x^2+10)^5)