What is xe^y+ye^z+2ln(x)-2-ln(8) ?

The solution to xe^y+ye^z+2ln(x)-2-ln(8) is xe^y+ye^z+ln((x^2)/8)-2

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simplify xe^y+ye^z+2ln(x)-2-ln(8)

simplify

x e^{y} + y e^{z} + 2 ln (x) - 2 - ln (8)

x e^{y} + y e^{z} + ln (\frac{x ^{2}}{8}) - 2

Solution steps

x e^{y} + y e^{z} + 2 ln (x) - 2 - ln (8)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= e^{y} x + e^{z} y + ln (x^{2}) - 2 - ln (8)

Apply log rule:

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

ln (x^{2}) - ln (8) = ln (\frac{x ^{2}}{8})

= x e^{y} + y e^{z} + ln (\frac{x ^{2}}{8}) - 2

5 \cdot ln (3 \cdot 45)

ln (c^{2} a)

ln (0.5 \cdot 1.7 \cdot 3.4 \cdot 5.7 \cdot 8.4)

lo g_{4} (6) - lo g_{4} (10) + lo g_{4} (x)

ln (\frac{35}{50})

What is xe^y+ye^z+2ln(x)-2-ln(8) ?
The solution to xe^y+ye^z+2ln(x)-2-ln(8) is xe^y+ye^z+ln((x^2)/8)-2