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

The solution to ln(2)-ln(5)-ln(1)+ln(4) is ln(8/5)

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

simplify

ln (2) - ln (5) - ln (1) + ln (4)

ln (\frac{8}{5})

Decimal Notation

0.47000 \dots

Solution steps

ln (2) - ln (5) - ln (1) + ln (4)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{2}{5} \cdot 4 = \frac{8}{5}

= ln (\frac{8}{5}) - ln (1)

Apply log rule:

lo g_{a} (1) = 0

= ln (\frac{8}{5}) - 0

ln (\frac{8}{5}) - 0 = ln (\frac{8}{5})

= ln (\frac{8}{5})

ln (\frac{1}{382})

ln (\frac{72}{129})

ln (\frac{5 w ^{2} v}{x + y})

ln_{e} (x^{\frac{1}{8}})

\frac{1}{5} x^{5} (ln (3) + 2 ln (x))

What is ln(2)-ln(5)-ln(1)+ln(4) ?
The solution to ln(2)-ln(5)-ln(1)+ln(4) is ln(8/5)