What is 2ln(5)-2ln(3) ?

The solution to 2ln(5)-2ln(3) is ln(25/9)

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simplify 2ln(5)-2ln(3)

simplify

2 ln (5) - 2 ln (3)

ln (\frac{25}{9})

Decimal Notation

1.02165 \dots

Solution steps

2 ln (5) - 2 ln (3)

Apply log rule:

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

2 ln (5) = ln (5^{2})

= ln (5^{2}) - 2 ln (3)

Apply log rule:

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

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

= ln (5^{2}) - ln (3^{2})

Apply log rule:

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

ln (5^{2}) - ln (3^{2}) = ln (\frac{5 ^{2}}{3 ^{2}})

= ln (\frac{5 ^{2}}{3 ^{2}})

\frac{5 ^{2}}{3 ^{2}} = \frac{25}{9}

= ln (\frac{25}{9})

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