What is 1/4 ln(5)+ln(2)-ln(3) ?

The solution to 1/4 ln(5)+ln(2)-ln(3) is ln((5^{1/4}*2)/3)

Popular >

simplify 1/4 ln(5)+ln(2)-ln(3)

simplify

\frac{1}{4} ln (5) + ln (2) - ln (3)

ln (\frac{5 ^{\frac{1}{4}} \cdot 2}{3})

Decimal Notation

- 0.00310 \dots

Solution steps

\frac{1}{4} ln (5) + ln (2) - ln (3)

Apply log rule:

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

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

= ln (5^{\frac{1}{4}}) + ln (2) - ln (3)

Apply log rule:

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

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

= ln (5^{\frac{1}{4}} \cdot 2) - ln (3)

Apply log rule:

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

ln (2 \cdot 5^{\frac{1}{4}}) - ln (3) = ln (\frac{2 \cdot 5 ^{\frac{1}{4}}}{3})

= ln (\frac{5 ^{\frac{1}{4}} \cdot 2}{3})

ln (\frac{( a + b )}{2})

ln (12 x^{2} + 15 x - 18) - ln (4 x - 3) - ln (x + 2)

ln (\frac{27}{150})

lo g_{10} (a) - 6 lo g_{10} (c)

- lo g_{3} (75 \cdot 1 0^{- 3})

What is 1/4 ln(5)+ln(2)-ln(3) ?
The solution to 1/4 ln(5)+ln(2)-ln(3) is ln((5^{1/4}*2)/3)