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Popular >

simplify 2ln(5)-3ln(2)-ln(20)

Solution

simplify

2 ln (5) - 3 ln (2) - ln (20)

Solution

ln (\frac{5}{32})

+1

Decimal Notation

- 1.85629 \dots

Solution steps

2 ln (5) - 3 ln (2) - ln (20)

Apply log rule:

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

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

= ln (5^{2}) - 3 ln (2) - ln (20)

Apply log rule:

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

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

= ln (5^{2}) - ln (2^{3}) - ln (20)

Apply log rule:

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

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

= ln (\frac{5 ^{2}}{2 ^{3}}) - ln (20)

\frac{5 ^{2}}{2 ^{3}} = \frac{25}{8}

= ln (\frac{25}{8}) - ln (20)

Apply log rule:

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

ln (\frac{25}{8}) - ln (20) = ln (\frac{\frac{25}{8}}{20})

= ln (\frac{\frac{25}{8}}{20})

\frac{\frac{25}{8}}{20} = \frac{5}{32}

= ln (\frac{5}{32})

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- lo g_{10} (1.37 \cdot 1 0^{- 4})

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ln (\frac{24}{109})

Frequently Asked Questions (FAQ)

What is 2ln(5)-3ln(2)-ln(20) ?
The solution to 2ln(5)-3ln(2)-ln(20) is ln(5/32)