What is ln((1-x)/((x+4)^4)) ?

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

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simplify ln((1-x)/((x+4)^4))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{3}{4 x ^{4} y})

lo g_{2} (5) + lo g_{2} (x) - lo g_{2} (3)

lo g_{10} (5 t)

8 lo g_{b} (x) + 9 lo g_{b} (z)

lo g_{4} (5) - lo g_{4} (9)

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