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

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

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

simplify

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

ln (\frac{3}{2})

Decimal Notation

0.40546 \dots

Solution steps

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

Apply log rule:

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

ln (3) + ln (2) = ln (3 \cdot 2)

= ln (3 \cdot 2) - ln (4)

Multiply the numbers:

3 \cdot 2 = 6

= ln (6) - ln (4)

Apply log rule:

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

ln (6) - ln (4) = ln (\frac{6}{4})

= ln (\frac{6}{4})

Cancel the common factor:

2

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

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ln (\frac{0.6}{3})

2 ln (y) + ln (x)