What is ln(1/125)+4ln(5)-2ln(1/5) ?

The solution to ln(1/125)+4ln(5)-2ln(1/5) is 3ln(5)

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simplify ln(1/125)+4ln(5)-2ln(1/5)

simplify

ln (\frac{1}{125}) + 4 ln (5) - 2 ln (\frac{1}{5})

3 ln (5)

Decimal Notation

4.82831 \dots

Solution steps

ln (\frac{1}{125}) + 4 ln (5) - 2 ln (\frac{1}{5})

Apply log rule:

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

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

= ln (\frac{1}{125}) + ln (5^{4}) - 2 ln (\frac{1}{5})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{1}{125}) + ln (5^{4}) = ln (5^{4} \cdot \frac{1}{125})

= ln (5^{4} \cdot \frac{1}{125}) - 2 ln (\frac{1}{5})

\frac{1}{125} \cdot 5^{4} = 5

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

Simplify

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

= ln (5) - (- 2 ln (5))

Apply rule

- (- a) = a

= ln (5) + 2 ln (5)

Add similar elements:

ln (5) + 2 ln (5) = 3 ln (5)

= 3 ln (5)

ln (\frac{1}{x}) - ln (x)

\frac{6}{5} ln \frac{y}{x} - 1 - \frac{1}{5} ln \frac{y}{x} + 4 + ln ∣ x ∣

0.77 + \frac{8.134 \cdot 298}{1 \cdot 96500} \cdot ln (\frac{1}{4})

ln (\frac{1}{2} e)

ln^{3} (x) - 3 ln (x)

What is ln(1/125)+4ln(5)-2ln(1/5) ?
The solution to ln(1/125)+4ln(5)-2ln(1/5) is 3ln(5)