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Popular >

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

Solution

simplify

2 ln (3) - 5 ln (2)

Solution

ln (\frac{9}{32})

+1

Decimal Notation

- 1.26851 \dots

Solution steps

2 ln (3) - 5 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{3 ^{2}}{2 ^{5}} = \frac{9}{32}

= ln (\frac{9}{32})

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Frequently Asked Questions (FAQ)

What is 2ln(3)-5ln(2) ?
The solution to 2ln(3)-5ln(2) is ln(9/32)