What is ln((e^{x+xyz})/(e^{x+xyz)+e^y}) ?

The solution to ln((e^{x+xyz})/(e^{x+xyz)+e^y}) is x+xyz-ln(e^{x+xyz}+e^y)

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simplify ln((e^{x+xyz})/(e^{x+xyz)+e^y})

simplify

ln (\frac{e ^{x + x yz}}{e ^{x + x yz} + e ^{y}})

x + x yz - ln (e^{x + x yz} + e^{y})

Solution steps

ln (\frac{e ^{x + x yz}}{e ^{x + x yz} + e ^{y}})

Apply log rule:

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

ln (\frac{e ^{x + x yz}}{e ^{x + x yz} + e ^{y}}) = ln (e^{x + x yz}) - ln (e^{x + x yz} + e^{y})

= ln (e^{x + x yz}) - ln (e^{y} + e^{x + x yz})

Apply log rule:

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

ln (e^{x + x yz}) = (x + x yz) ln (e)

= (x + x yz) ln (e) - ln (e^{x + x yz} + e^{y})

(x + x yz) ln (e) = x + x yz

= x + x yz - ln (e^{y} + e^{x + x yz})

0.2 lo g_{2} (0.2) + 0.8 lo g_{2} (0.8)

- lo g_{10} (3.8 \cdot 1 0^{- 3})

\frac{ln ( 10 )}{2 ln ( 2 ) - ln ( 5 )}

\frac{9}{10} ln (30)

What is ln((e^{x+xyz})/(e^{x+xyz)+e^y}) ?
The solution to ln((e^{x+xyz})/(e^{x+xyz)+e^y}) is x+xyz-ln(e^{x+xyz}+e^y)