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Popular >

simplify 3ln(3)-2ln(5)-ln(7)

Solution

simplify

3 ln (3) - 2 ln (5) - ln (7)

Solution

ln (\frac{27}{175})

+1

Decimal Notation

- 1.86894 \dots

Solution steps

3 ln (3) - 2 ln (5) - ln (7)

Apply log rule:

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

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

= ln (3^{3}) - 2 ln (5) - ln (7)

Apply log rule:

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

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

= ln (3^{3}) - ln (5^{2}) - ln (7)

Apply log rule:

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

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

= ln (\frac{3 ^{3}}{5 ^{2}}) - ln (7)

\frac{3 ^{3}}{5 ^{2}} = \frac{27}{25}

= ln (\frac{27}{25}) - ln (7)

Apply log rule:

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

ln (\frac{27}{25}) - ln (7) = ln (\frac{\frac{27}{25}}{7})

= ln (\frac{\frac{27}{25}}{7})

\frac{\frac{27}{25}}{7} = \frac{27}{175}

= ln (\frac{27}{175})

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Frequently Asked Questions (FAQ)

What is 3ln(3)-2ln(5)-ln(7) ?
The solution to 3ln(3)-2ln(5)-ln(7) is ln(27/175)