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

The solution to 2ln(3)-4ln(7) is ln(9/2401)

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

simplify

2 ln (3) - 4 ln (7)

ln (\frac{9}{2401})

Decimal Notation

- 5.58641 \dots

Solution steps

2 ln (3) - 4 ln (7)

Apply log rule:

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

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

= ln (3^{2}) - 4 ln (7)

Apply log rule:

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

4 ln (7) = ln (7^{4})

= ln (3^{2}) - ln (7^{4})

Apply log rule:

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

ln (3^{2}) - ln (7^{4}) = ln (\frac{3 ^{2}}{7 ^{4}})

= ln (\frac{3 ^{2}}{7 ^{4}})

\frac{3 ^{2}}{7 ^{4}} = \frac{9}{2401}

= ln (\frac{9}{2401})

\frac{( - 12 [ ln ( 9.5 + 2 x ) - ln ( 6.5 + 2 x ) ] ) ^{'}}{4}

lo g_{b} (8) + lo g_{b} (3)

e^{x y} - ln (\frac{x ^{2}}{y ^{2}})

2 ln (3) - 4 ln (6)

6 lo g_{2} (x) - 30 lo g_{2} (y)