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

The solution to 5ln(5)-3ln(3) is ln(3125/27)

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

simplify

5 ln (5) - 3 ln (3)

ln (\frac{3125}{27})

Decimal Notation

4.75135 \dots

Solution steps

5 ln (5) - 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}) - 3 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{5 ^{5}}{3 ^{3}} = \frac{3125}{27}

= ln (\frac{3125}{27})

ln (\frac{1 + e ^{x}}{1 - e ^{x}})

\frac{1}{6} (ln ∣ x ∣ - ln (x + 6))

2 ln (x) - 4 lo g_{e} (\frac{1}{y}) - 3 lo g_{e} (x) y

3 ln (5) - \frac{1}{2} ln (4) + ln (8)

lo g_{4} (\frac{4 a}{b})