What is 2ln(x^{0.5}y^{0.5}) ?

The solution to 2ln(x^{0.5}y^{0.5}) is ln(x)+ln(y)

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simplify 2ln(x^{0.5}y^{0.5})

simplify

2 ln (x^{0.5} y^{0.5})

ln (x) + ln (y)

Solution steps

2 ln (x^{0.5} y^{0.5})

Apply log rule:

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

2 ln (x^{0.5} y^{0.5}) = 2 ln (x^{0.5}) + 2 ln (y^{0.5})

= 2 ln (x^{0.5}) + 2 ln (y^{0.5})

Apply log rule:

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

ln (x^{0.5}) = 0.5 ln (x)

= 2 \cdot 0.5 ln (x) + 2 ln (y^{0.5})

Apply log rule:

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

ln (y^{0.5}) = 0.5 ln (y)

= 2 \cdot 0.5 ln (x) + 2 \cdot 0.5 ln (y)

Multiply:

2 \cdot 0.5 ln (x) = ln (x)

= ln (x) + 2 \cdot 0.5 ln (y)

Multiply:

2 \cdot 0.5 ln (y) = ln (y)

= ln (x) + ln (y)

- \frac{2}{3} lo g_{10} (x) - 2 lo g_{10} (y)

1 + \frac{1}{2} lo g_{10} (p + 4) - lo g_{10} (x)

7 ln (x + 9) - 8 ln (x)

ln (\frac{y}{x} - 4) + 6 (\frac{1}{5} ln (\frac{y}{x} - 1) - \frac{1}{5} ln (\frac{y}{x} + 4)) + ln (x)

\frac{3}{8} \cdot ln (\frac{8}{3}) + (\frac{5}{16} \cdot ln (\frac{16}{5})) \cdot 2

What is 2ln(x^{0.5}y^{0.5}) ?
The solution to 2ln(x^{0.5}y^{0.5}) is ln(x)+ln(y)