What is ln((sqrt(x)y^5)/((z+1)^4)) ?

The solution to ln((sqrt(x)y^5)/((z+1)^4)) is ln(sqrt(x))+5ln(y)-4ln(z+1)

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simplify ln((sqrt(x)y^5)/((z+1)^4))

simplify

ln (\frac{x y ^{5}}{( z + 1 ) ^{4}})

ln (x) + 5 ln (y) - 4 ln (z + 1)

Solution steps

ln (\frac{x y ^{5}}{( z + 1 ) ^{4}})

Apply log rule:

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

ln (\frac{x y ^{5}}{( z + 1 ) ^{4}}) = ln (x y^{5}) - ln ((z + 1)^{4})

= ln (y^{5} x) - ln ((z + 1)^{4})

Apply log rule:

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

ln ((z + 1)^{4}) = 4 ln (z + 1)

= ln (x y^{5}) - 4 ln (z + 1)

Apply log rule:

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

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

= ln (x) + ln (y^{5}) - 4 ln (z + 1)

Apply log rule:

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

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

= ln (x) + 5 ln (y) - 4 ln (z + 1)

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

- lo g_{10} (2.54 \cdot 1 0^{- 2})

ln (0.1 e^{0.1})

lo g_{10} (2) 5

ln (\frac{1 + cos ( x )}{1 - cos ( x )})

What is ln((sqrt(x)y^5)/((z+1)^4)) ?
The solution to ln((sqrt(x)y^5)/((z+1)^4)) is ln(sqrt(x))+5ln(y)-4ln(z+1)