What is (ln(2)-2ln(5))-(ln(1)-2ln(4)) ?

The solution to (ln(2)-2ln(5))-(ln(1)-2ln(4)) is ln(2/25)+4ln(2)

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simplify (ln(2)-2ln(5))-(ln(1)-2ln(4))

simplify

(ln (2) - 2 ln (5)) - (ln (1) - 2 ln (4))

ln (\frac{2}{25}) + 4 ln (2)

Decimal Notation

0.24686 \dots

Solution steps

(ln (2) - 2 ln (5)) - (ln (1) - 2 ln (4))

Apply log rule:

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

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

= (ln (2) - ln (5^{2})) - (ln (1) - 2 ln (4))

Apply log rule:

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

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

= ln (\frac{2}{5 ^{2}}) - (ln (1) - 2 ln (4))

5^{2} = 25

= ln (\frac{2}{25}) - (ln (1) - 2 ln (4))

- (ln (1) - 2 ln (4)) = 4 ln (2)

= ln (\frac{2}{25}) + 4 ln (2)

2 ln (x) + ln (v^{2} + 2)

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

ln (\frac{30.3}{10.6})

- ln ∣ x ∣ - \frac{3}{x} + ln ∣ x - 1 ∣

lo g_{\frac{1}{3}} (\frac{1}{15})

What is (ln(2)-2ln(5))-(ln(1)-2ln(4)) ?
The solution to (ln(2)-2ln(5))-(ln(1)-2ln(4)) is ln(2/25)+4ln(2)