What is ln((sqrt(x))/((x+1)^9(x+8)^4)) ?

The solution to ln((sqrt(x))/((x+1)^9(x+8)^4)) is ln(sqrt(x))-9ln(x+1)-4ln(x+8)

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simplify ln((sqrt(x))/((x+1)^9(x+8)^4))

simplify

ln (\frac{x}{( x + 1 ) ^{9} ( x + 8 ) ^{4}})

ln (x) - 9 ln (x + 1) - 4 ln (x + 8)

Solution steps

ln (\frac{x}{( x + 1 ) ^{9} ( x + 8 ) ^{4}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x}{( x + 1 ) ^{9} ( x + 8 ) ^{4}}) = ln (x) - ln ((x + 1)^{9} (x + 8)^{4})

= ln (x) - ln ((x + 1)^{9} (x + 8)^{4})

Apply log rule:

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

ln ((x + 1)^{9} (x + 8)^{4}) = ln ((x + 1)^{9}) + ln ((x + 8)^{4})

= ln (x) - (ln ((x + 1)^{9}) + ln ((x + 8)^{4}))

Apply log rule:

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

ln ((x + 1)^{9}) = 9 ln (x + 1)

= ln (x) - (9 ln (x + 1) + ln ((x + 8)^{4}))

Apply log rule:

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

ln ((x + 8)^{4}) = 4 ln (x + 8)

= ln (x) - (9 ln (x + 1) + 4 ln (x + 8))

- (9 ln (x + 1) + 4 ln (x + 8)) : - 9 ln (x + 1) - 4 ln (x + 8)

= ln (x) - 9 ln (x + 1) - 4 ln (x + 8)

3 ln (x + 6) - 7 ln (x)

ln (\frac{0.45}{0.42})

3 lo g_{4} (a) - 5 lo g_{4} (b)

lo g_{10} (\frac{e ^{- y} y ^{x}}{x !})

ln (\frac{x}{1200 - x})

What is ln((sqrt(x))/((x+1)^9(x+8)^4)) ?
The solution to ln((sqrt(x))/((x+1)^9(x+8)^4)) is ln(sqrt(x))-9ln(x+1)-4ln(x+8)