What is ln(8)+5ln(x)+4ln(x^2+3) ?

The solution to ln(8)+5ln(x)+4ln(x^2+3) is ln(8x^5(x^2+3)^4)

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simplify ln(8)+5ln(x)+4ln(x^2+3)

simplify

ln (8) + 5 ln (x) + 4 ln (x^{2} + 3)

ln (8 x^{5} (x^{2} + 3)^{4})

Solution steps

ln (8) + 5 ln (x) + 4 ln (x^{2} + 3)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln (8) + ln (x^{5}) + 4 ln (x^{2} + 3)

Apply log rule:

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

ln (8) + ln (x^{5}) = ln (8 x^{5})

= ln (8 x^{5}) + 4 ln (x^{2} + 3)

Apply log rule:

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

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

= ln (8 x^{5}) + ln ((x^{2} + 3)^{4})

Apply log rule:

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

ln (8 x^{5}) + ln ((x^{2} + 3)^{4}) = ln (8 x^{5} (x^{2} + 3)^{4})

= ln (8 x^{5} (x^{2} + 3)^{4})

- 2 ln (2^{2}) + 2 ln (x)

ln (cos (5^{x}) 5^{x} ln (5))

ln (x - 6) - ln (x + 6)

ln (\frac{1}{2}) \cdot 20

ln (\frac{8235744}{8831079})

What is ln(8)+5ln(x)+4ln(x^2+3) ?
The solution to ln(8)+5ln(x)+4ln(x^2+3) is ln(8x^5(x^2+3)^4)