What is ln(2)-ln(4)-ln(1)+ln(3) ?

The solution to ln(2)-ln(4)-ln(1)+ln(3) is ln(3/2)

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simplify ln(2)-ln(4)-ln(1)+ln(3)

simplify

ln (2) - ln (4) - ln (1) + ln (3)

ln (\frac{3}{2})

Decimal Notation

0.40546 \dots

Solution steps

ln (2) - ln (4) - ln (1) + ln (3)

Apply log rule:

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

ln (3) - ln (4) = ln (\frac{3}{4})

= ln (2) + ln (\frac{3}{4}) - ln (1)

Apply log rule:

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

ln (2) + ln (\frac{3}{4}) = ln (2 \cdot \frac{3}{4})

= ln (2 \cdot \frac{3}{4}) - ln (1)

2 \cdot \frac{3}{4} = \frac{3}{2}

= ln (\frac{3}{2}) - ln (1)

Apply log rule:

lo g_{a} (1) = 0

= ln (\frac{3}{2}) - 0

ln (\frac{3}{2}) - 0 = ln (\frac{3}{2})

= ln (\frac{3}{2})

ln (\frac{7 x ^{2}}{10})

2 ln (4) - 2 ln (5)

ln (\frac{x ^{17} x - 1}{3 x - 10})

lo g_{b} (\frac{25}{9})

2 lo g_{3} (k) - 3 - lo g_{3} (x)

What is ln(2)-ln(4)-ln(1)+ln(3) ?
The solution to ln(2)-ln(4)-ln(1)+ln(3) is ln(3/2)