What is ln(x^6(x+9)^7(x^2+8)^2) ?

The solution to ln(x^6(x+9)^7(x^2+8)^2) is 6ln(x)+7ln(x+9)+2ln(x^2+8)

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simplify ln(x^6(x+9)^7(x^2+8)^2)

simplify

ln (x^{6} (x + 9)^{7} (x^{2} + 8)^{2})

6 ln (x) + 7 ln (x + 9) + 2 ln (x^{2} + 8)

Solution steps

ln (x^{6} (x + 9)^{7} (x^{2} + 8)^{2})

Apply log rule:

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

ln (x^{6} (x + 9)^{7} (x^{2} + 8)^{2}) = ln (x^{6}) + ln ((x + 9)^{7}) + ln ((x^{2} + 8)^{2})

= ln (x^{6}) + ln ((x + 9)^{7}) + ln ((x^{2} + 8)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{6}) = 6 ln (x)

= 6 ln (x) + ln ((x + 9)^{7}) + ln ((x^{2} + 8)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 9)^{7}) = 7 ln (x + 9)

= 6 ln (x) + 7 ln (x + 9) + ln ((x^{2} + 8)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 6 ln (x) + 7 ln (x + 9) + 2 ln (x^{2} + 8)

96 - 10 \cdot lo g_{10} (\frac{4 \cdot 3.14 \cdot 4 ^{2}}{2})

ln ((- 0.34)^{23.2505} (- 0.86)^{7.84805})

- lo g_{10} (1.48 \cdot 1 0^{- 3})

3 ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ 3 x - 6 ∣ + c

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (- 1 - \frac{1}{4} - \frac{3}{4})

What is ln(x^6(x+9)^7(x^2+8)^2) ?
The solution to ln(x^6(x+9)^7(x^2+8)^2) is 6ln(x)+7ln(x+9)+2ln(x^2+8)