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

The solution to ln(3)+ln(7)-ln(2)-2ln(4) is ln(21/32)

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

simplify

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

ln (\frac{21}{32})

Decimal Notation

- 0.42121 \dots

Solution steps

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

Apply log rule:

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

ln (3) + ln (7) = ln (3 \cdot 7)

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

Multiply the numbers:

3 \cdot 7 = 21

= ln (21) - ln (2) - 2 ln (4)

Apply log rule:

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

ln (21) - ln (2) = ln (\frac{21}{2})

= ln (\frac{21}{2}) - 2 ln (4)

Apply log rule:

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

2 ln (4) = ln (4^{2})

= ln (\frac{21}{2}) - ln (4^{2})

Apply log rule:

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

ln (\frac{21}{2}) - ln (4^{2}) = ln (\frac{\frac{21}{2}}{4 ^{2}})

= ln (\frac{\frac{21}{2}}{4 ^{2}})

\frac{\frac{21}{2}}{4 ^{2}} = \frac{21}{32}

= ln (\frac{21}{32})

ln (\frac{4 x ^{4} + 4 x}{x ^{2} + 2 x})

- (\frac{5}{6}) lo g_{2} (\frac{5}{6}) - (\frac{1}{6}) lo g_{2} (\frac{1}{6})

ln (\frac{2}{6})

3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

4 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

What is ln(3)+ln(7)-ln(2)-2ln(4) ?
The solution to ln(3)+ln(7)-ln(2)-2ln(4) is ln(21/32)