What is 1/2 ln(5)-1/2 ln(4) ?

The solution to 1/2 ln(5)-1/2 ln(4) is ln((5^{1/2})/2)

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simplify 1/2 ln(5)-1/2 ln(4)

simplify

\frac{1}{2} ln (5) - \frac{1}{2} ln (4)

ln (\frac{5 ^{\frac{1}{2}}}{2})

Decimal Notation

0.11157 \dots

Solution steps

\frac{1}{2} ln (5) - \frac{1}{2} ln (4)

Apply log rule:

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

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

= ln (5^{\frac{1}{2}}) - \frac{1}{2} ln (4)

Apply log rule:

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

\frac{1}{2} ln (4) = ln (4^{\frac{1}{2}})

= ln (5^{\frac{1}{2}}) - ln (4^{\frac{1}{2}})

Apply log rule:

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

ln (5^{\frac{1}{2}}) - ln (4^{\frac{1}{2}}) = ln (\frac{5 ^{\frac{1}{2}}}{4 ^{\frac{1}{2}}})

= ln (\frac{5 ^{\frac{1}{2}}}{4 ^{\frac{1}{2}}})

4^{\frac{1}{2}} = 2

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

3 + 2 ln (2) - 2 ln (5)

ln (\frac{a + b x}{a - b x})

2 ln (x) - 3 ln (x + 1) - ln (x)

3 lo g_{a} (2) + lo g_{a} (c) - 2 lo g_{a} (d)

- lo g_{10} (1.25 \cdot 1 0^{- 10})

What is 1/2 ln(5)-1/2 ln(4) ?
The solution to 1/2 ln(5)-1/2 ln(4) is ln((5^{1/2})/2)