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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (6 \cdot 7)

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

ln (x - 3) - 2 ln (x + 12) - ln (x)

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

ln (- e^{- y} (y + 1))

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