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

The solution to 1/4 ln(5/3)+1/4 ln(5) is 1/4 ln(25/3)

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

simplify

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

\frac{1}{4} ln (\frac{25}{3})

Decimal Notation

0.53006 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Rewrite as

= ln ((\frac{25}{3})^{\frac{1}{4}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{4} ln (\frac{25}{3})

20 lo g_{10} (\frac{P}{2 \cdot 1 0 ^{- 4}})

\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣

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

ln (p) + ln (1 - p)

- lo g_{10} (7.8 \cdot 1 0^{- 3})

What is 1/4 ln(5/3)+1/4 ln(5) ?
The solution to 1/4 ln(5/3)+1/4 ln(5) is 1/4 ln(25/3)