What is 2ln(2)-1/2 ln(9) ?

The solution to 2ln(2)-1/2 ln(9) is ln(4/3)

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simplify 2ln(2)-1/2 ln(9)

simplify

2 ln (2) - \frac{1}{2} ln (9)

ln (\frac{4}{3})

Decimal Notation

0.28768 \dots

Solution steps

2 ln (2) - \frac{1}{2} ln (9)

Apply log rule:

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

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

= ln (2^{2}) - \frac{1}{2} ln (9)

Apply log rule:

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

\frac{1}{2} ln (9) = ln (9^{\frac{1}{2}})

= ln (2^{2}) - ln (9^{\frac{1}{2}})

Apply log rule:

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

ln (2^{2}) - ln (9^{\frac{1}{2}}) = ln (\frac{2 ^{2}}{9 ^{\frac{1}{2}}})

= ln (\frac{2 ^{2}}{9 ^{\frac{1}{2}}})

\frac{2 ^{2}}{9 ^{\frac{1}{2}}} = \frac{4}{3}

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

ln (y) - ln (c)

ln (18) + ln (4) - 2 ln (3)

2 ln (c) - 3 ln (d) + ln (b)

ln (\frac{306.34}{1173.15})

e^{2 (l n (x) - l n (1 - x))}