What is ln(4)+ln(7)-2ln(3) ?

The solution to ln(4)+ln(7)-2ln(3) is ln(28/9)

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simplify ln(4)+ln(7)-2ln(3)

simplify

ln (4) + ln (7) - 2 ln (3)

ln (\frac{28}{9})

Decimal Notation

1.13497 \dots

Solution steps

ln (4) + ln (7) - 2 ln (3)

Apply log rule:

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

ln (4) + ln (7) = ln (4 \cdot 7)

= ln (4 \cdot 7) - 2 ln (3)

Multiply the numbers:

4 \cdot 7 = 28

= ln (28) - 2 ln (3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (3) = ln (3^{2})

= ln (28) - ln (3^{2})

Apply log rule:

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

ln (28) - ln (3^{2}) = ln (\frac{28}{3 ^{2}})

= ln (\frac{28}{3 ^{2}})

3^{2} = 9

= ln (\frac{28}{9})

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