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Popular >

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

Solution

simplify

5 ln (5) - 4 ln (4) - 3 ln (3)

Solution

ln (\frac{3125}{6912})

+1

Decimal Notation

- 0.79382 \dots

Solution steps

5 ln (5) - 4 ln (4) - 3 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{5 ^{5}}{4 ^{4}} = \frac{3125}{256}

= ln (\frac{3125}{256}) - 3 ln (3)

Apply log rule:

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

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

= ln (\frac{3125}{256}) - ln (3^{3})

Apply log rule:

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

ln (\frac{3125}{256}) - ln (3^{3}) = ln (\frac{\frac{3125}{256}}{3 ^{3}})

= ln (\frac{\frac{3125}{256}}{3 ^{3}})

\frac{\frac{3125}{256}}{3 ^{3}} = \frac{3125}{6912}

= ln (\frac{3125}{6912})

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Frequently Asked Questions (FAQ)

What is 5ln(5)-4ln(4)-3ln(3) ?
The solution to 5ln(5)-4ln(4)-3ln(3) is ln(3125/6912)