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Popular >

simplify 1/2 ln(50)+1/2 ln(1-1/2)

Solution

simplify

\frac{1}{2} ln (50) + \frac{1}{2} ln (1 - \frac{1}{2})

Solution

ln (5)

+1

Decimal Notation

1.60943 \dots

Solution steps

\frac{1}{2} ln (50) + \frac{1}{2} ln (1 - \frac{1}{2})

Apply log rule:

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

\frac{1}{2} ln (50) = ln (5 0^{\frac{1}{2}})

= ln (5 0^{\frac{1}{2}}) + \frac{1}{2} ln (- \frac{1}{2} + 1)

Apply log rule:

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

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

= ln (5 0^{\frac{1}{2}}) + ln ((- \frac{1}{2} + 1)^{\frac{1}{2}})

Apply log rule:

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

ln (5 0^{\frac{1}{2}}) + ln ((1 - \frac{1}{2})^{\frac{1}{2}}) = ln (5 0^{\frac{1}{2}} (- \frac{1}{2} + 1)^{\frac{1}{2}})

= ln (5 0^{\frac{1}{2}} (- \frac{1}{2} + 1)^{\frac{1}{2}})

5 0^{\frac{1}{2}} (1 - \frac{1}{2})^{\frac{1}{2}} = 5

= ln (5)

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Frequently Asked Questions (FAQ)

What is 1/2 ln(50)+1/2 ln(1-1/2) ?
The solution to 1/2 ln(50)+1/2 ln(1-1/2) is ln(5)