What is ln(x^2(x+6)^7(x^2+5)^4) ?

The solution to ln(x^2(x+6)^7(x^2+5)^4) is 2ln(x)+7ln(x+6)+4ln(x^2+5)

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simplify ln(x^2(x+6)^7(x^2+5)^4)

simplify

ln (x^{2} (x + 6)^{7} (x^{2} + 5)^{4})

2 ln (x) + 7 ln (x + 6) + 4 ln (x^{2} + 5)

Solution steps

ln (x^{2} (x + 6)^{7} (x^{2} + 5)^{4})

Apply log rule:

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

ln (x^{2} (x + 6)^{7} (x^{2} + 5)^{4}) = ln (x^{2}) + ln ((x + 6)^{7}) + ln ((x^{2} + 5)^{4})

= ln (x^{2}) + ln ((x + 6)^{7}) + ln ((x^{2} + 5)^{4})

Apply log rule:

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

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

= 2 ln (x) + ln ((x + 6)^{7}) + ln ((x^{2} + 5)^{4})

Apply log rule:

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

ln ((x + 6)^{7}) = 7 ln (x + 6)

= 2 ln (x) + 7 ln (x + 6) + ln ((x^{2} + 5)^{4})

Apply log rule:

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

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

= 2 ln (x) + 7 ln (x + 6) + 4 ln (x^{2} + 5)

1004 \cdot ln (\frac{100}{930}) - 287 \cdot ln (\frac{3}{4})

20 lo g_{10} (\frac{2 \cdot 1 0 ^{- 5}}{1 0 ^{- 6}})

- \frac{1}{9} ln (\frac{e ^{- 18} - 1}{- 18})

lo g_{e} (\frac{3 x - 1}{2 x + 2})

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What is ln(x^2(x+6)^7(x^2+5)^4) ?
The solution to ln(x^2(x+6)^7(x^2+5)^4) is 2ln(x)+7ln(x+6)+4ln(x^2+5)