What is cos(xy+yz)+ln((xy)/z) ?

The solution to cos(xy+yz)+ln((xy)/z) is cos(xy+yz)++ln(x)+ln(y)-ln(z)

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simplify cos(xy+yz)+ln((xy)/z)

simplify

cos (x y + yz) + ln (\frac{x y}{z})

cos (x y + yz) + + ln (x) + ln (y) - ln (z)

Solution steps

cos (x y + yz) + ln (\frac{x y}{z})

Apply log rule:

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

ln (\frac{x y}{z}) = ln (x y) - ln (z)

= cos (x y + yz) + + ln (x y) - ln (z)

Apply log rule:

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

ln (x y) = ln (x) + ln (y)

= cos (x y + yz) + + ln (x) + ln (y) - ln (z)

3 ln (2) - \frac{7 ln ( 3 )}{4}

7 lo g_{x} (y) + 6 lo g_{x} (z)

- lo g_{10} (9 \cdot 1 0^{- 13})

- ln (x) + ln (x - 2)

14 - lo g_{10} (1.8 \cdot 1 0^{- 5})

What is cos(xy+yz)+ln((xy)/z) ?
The solution to cos(xy+yz)+ln((xy)/z) is cos(xy+yz)++ln(x)+ln(y)-ln(z)