What is 5/2 ln(15/4) ?

The solution to 5/2 ln(15/4) is 5/2 ln(15)-5ln(2)

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simplify 5/2 ln(15/4)

simplify

\frac{5}{2} ln (\frac{15}{4})

\frac{5}{2} ln (15) - 5 ln (2)

Decimal Notation

3.30438 \dots

Solution steps

\frac{5}{2} ln (\frac{15}{4})

Apply log rule:

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

ln (\frac{15}{4}) = ln (15) - ln (4)

= \frac{5}{2} (ln (15) - ln (4))

ln (4) = 2 ln (2)

= \frac{5}{2} (ln (15) - 2 ln (2))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{5}{2}, b = ln (15), c = 2 ln (2)

= \frac{5}{2} ln (15) - \frac{5}{2} \cdot 2 ln (2)

= \frac{5}{2} ln (15) - 2 \cdot \frac{5}{2} ln (2)

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

= \frac{5}{2} ln (15) - 5 ln (2)

lo g_{7} (343 x)

ln (\frac{6 x - 5}{x + 4})

lo g_{3} (4 x)

2 lo g_{a} (z + 6) + lo g_{a} (3 z + 5)

lo g_{5} (\frac{5}{y})