What is 3+2ln(2)-2ln(5) ?

The solution to 3+2ln(2)-2ln(5) is 3+ln(4/25)

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

simplify

3 + 2 ln (2) - 2 ln (5)

3 + ln (\frac{4}{25})

Decimal Notation

1.16741 \dots

Solution steps

3 + 2 ln (2) - 2 ln (5)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{2 ^{2}}{5 ^{2}} = \frac{4}{25}

= 3 + ln (\frac{4}{25})

ln (\frac{a + b x}{a - b x})

2 ln (x) - 3 ln (x + 1) - ln (x)

3 lo g_{a} (2) + lo g_{a} (c) - 2 lo g_{a} (d)

- lo g_{10} (1.25 \cdot 1 0^{- 10})

\frac{1}{2} ln (5) - \frac{1}{2} ln (2)