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Popular >

simplify 4ln(2)-5ln(3)

Solution

simplify

4 ln (2) - 5 ln (3)

Solution

ln (\frac{16}{243})

+1

Decimal Notation

- 2.72047 \dots

Solution steps

4 ln (2) - 5 ln (3)

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (2^{4}) - 5 ln (3)

Apply log rule:

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

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

= ln (2^{4}) - ln (3^{5})

Apply log rule:

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

ln (2^{4}) - ln (3^{5}) = ln (\frac{2 ^{4}}{3 ^{5}})

= ln (\frac{2 ^{4}}{3 ^{5}})

\frac{2 ^{4}}{3 ^{5}} = \frac{16}{243}

= ln (\frac{16}{243})

Popular Examples

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10 \cdot lo g_{10} (1 0^{\frac{a}{10}} - 1 0^{\frac{b}{10}})

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lo g_{10} (\frac{m}{7})

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

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Frequently Asked Questions (FAQ)

What is 4ln(2)-5ln(3) ?
The solution to 4ln(2)-5ln(3) is ln(16/243)