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Popular >

simplify 1/2 ln(2)+1/2 ln(3)

Solution

simplify

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

Solution

\frac{1}{2} ln (6)

+1

Decimal Notation

0.89587 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

\frac{1}{2} ln (3) = ln (3^{\frac{1}{2}})

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

Apply log rule:

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

ln (2^{\frac{1}{2}}) + ln (3^{\frac{1}{2}}) = ln (2^{\frac{1}{2}} \cdot 3^{\frac{1}{2}})

= ln (2^{\frac{1}{2}} \cdot 3^{\frac{1}{2}})

2^{\frac{1}{2}} \cdot 3^{\frac{1}{2}} = 6

= ln (6)

Rewrite as

= ln (6^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} ln (6)

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Frequently Asked Questions (FAQ)

What is 1/2 ln(2)+1/2 ln(3) ?
The solution to 1/2 ln(2)+1/2 ln(3) is 1/2 ln(6)