What is 1/2 ln(10)+1/2 ln(20) ?

The solution to 1/2 ln(10)+1/2 ln(20) is ln(10sqrt(2))

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simplify 1/2 ln(10)+1/2 ln(20)

simplify

\frac{1}{2} ln (10) + \frac{1}{2} ln (20)

ln (102)

Decimal Notation

2.64915 \dots

Solution steps

\frac{1}{2} ln (10) + \frac{1}{2} ln (20)

Apply log rule:

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

\frac{1}{2} ln (10) = ln (1 0^{\frac{1}{2}})

= ln (1 0^{\frac{1}{2}}) + \frac{1}{2} ln (20)

Apply log rule:

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

\frac{1}{2} ln (20) = ln (2 0^{\frac{1}{2}})

= ln (1 0^{\frac{1}{2}}) + ln (2 0^{\frac{1}{2}})

Apply log rule:

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

ln (1 0^{\frac{1}{2}}) + ln (2 0^{\frac{1}{2}}) = ln (1 0^{\frac{1}{2}} \cdot 2 0^{\frac{1}{2}})

= ln (1 0^{\frac{1}{2}} \cdot 2 0^{\frac{1}{2}})

1 0^{\frac{1}{2}} \cdot 2 0^{\frac{1}{2}} = 102

= ln (102)

3 ln (\frac{1}{2} 3) + 1

ln (x^{2}) - ln (y^{2}) + ln (l^{2})

lo g_{10} ((\frac{1}{4})_{2}) + 1

ln (8) - ln (e^{y})

ln (\frac{343}{293})

What is 1/2 ln(10)+1/2 ln(20) ?
The solution to 1/2 ln(10)+1/2 ln(20) is ln(10sqrt(2))