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

The solution to 1/2 ln(5)-1/2 ln(2) is 1/2 ln(5/2)

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

simplify

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

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

Decimal Notation

0.45814 \dots

Solution steps

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

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 (2)

Apply log rule:

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

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

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

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

Combine same powers :

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

Rewrite as

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

ln (5 e^{- 4 t})

0.026 ln (\frac{5 \cdot 1 0 ^{- 4}}{1 0 ^{- 12}})

\frac{ln ( 16 ) - ln ( 10 )}{ln ( 8 )} \cdot ln (10)

lo g_{6} ((\frac{12}{7})^{5})^{5}

lo g_{10} (\frac{x ^{6} y ^{18}}{z ^{14}})

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