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Popular >

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

Solution

simplify

2 ln (3) - 4 ln (5)

Solution

ln (\frac{9}{625})

+1

Decimal Notation

- 4.24052 \dots

Solution steps

2 ln (3) - 4 ln (5)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{3 ^{2}}{5 ^{4}} = \frac{9}{625}

= ln (\frac{9}{625})

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Frequently Asked Questions (FAQ)

What is 2ln(3)-4ln(5) ?
The solution to 2ln(3)-4ln(5) is ln(9/625)