simplify ln(4 1/16)

Solution

simplify

ln (4 \frac{1}{16})

ln (65) - 4 ln (2)

Decimal Notation

1.40179 \dots

Solution steps

ln (4 \frac{1}{16})

Convert mixed numbers to improper fractions:

4 \frac{1}{16} = \frac{65}{16}

= ln (\frac{65}{16})

Apply log rule:

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

ln (\frac{65}{16}) = ln (65) - ln (16)

= ln (65) - ln (16)

ln (16) = 4 ln (2)

= ln (65) - 4 ln (2)

5 lo g_{6} (x) - 3 lo g_{6} (y)

lo g_{10} (\frac{x}{100})

- lo g_{10} (5 \cdot 1 0^{- 5})

lo g_{3} (\frac{x ^{4}}{x + 2})