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Popular >

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

Solution

simplify

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

Solution

ln (\frac{12}{5})

+1

Decimal Notation

0.87546 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{2 ^{2}}{\frac{5}{3}} = \frac{12}{5}

= ln (\frac{12}{5})

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Frequently Asked Questions (FAQ)

What is 2ln(2)-ln(5/3) ?
The solution to 2ln(2)-ln(5/3) is ln(12/5)