simplify ln(5/4)+1

Solution

simplify

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

ln (5) - 2 ln (2) + 1

Decimal Notation

1.22314 \dots

Solution steps

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

Apply log rule:

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

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

= ln (5) - ln (4) + 1

ln (4) = 2 ln (2)

= ln (5) - 2 ln (2) + 1

lo g_{10} ((1 + i \cdot 3)^{2022})

2 ln (5) + (- \frac{1}{5}) + 3 ln (6) - (- 2 ln (1) - 1 + 3 ln (2))

- lo g_{10} (6.656 \cdot 1 0^{- 5})

(\frac{1}{2}) (ln (11 + 22 (6)) - ln (11 - 22 (6)))

\frac{1}{2} lo g_{12} (2)