What is ln((10/3)/(3*3.1)) ?

The solution to ln((10/3)/(3*3.1)) is ln(10)-2ln(3)-ln(3.1)

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simplify ln((10/3)/(3*3.1))

simplify

ln (\frac{\frac{10}{3}}{3 \cdot 3.1})

ln (10) - 2 ln (3) - ln (3.1)

Decimal Notation

- 1.02604 \dots

Solution steps

ln (\frac{\frac{10}{3}}{3 \cdot 3.1})

Apply log rule:

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

ln (\frac{\frac{10}{3}}{3 \cdot 3.1}) = ln (\frac{10}{3}) - ln (3 \cdot 3.1)

= ln (\frac{10}{3}) - ln (3 \cdot 3.1)

Apply log rule:

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

ln (\frac{10}{3}) = ln (10) - ln (3)

= ln (10) - ln (3) - ln (3 \cdot 3.1)

Apply log rule:

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

ln (3 \cdot 3.1) = ln (3) + ln (3.1)

= ln (10) - ln (3) - (ln (3) + ln (3.1))

- (ln (3) + ln (3.1)) : - ln (3) - ln (3.1)

= ln (10) - ln (3) - ln (3) - ln (3.1)

Add similar elements:

- ln (3) - ln (3) = - 2 ln (3)

= ln (10) - 2 ln (3) - ln (3.1)

ln (19) - ln (15)

ln (θ (1 - θ))

ln ∣ y ∣ - ln ∣ y - 2 ∣

2 lo g_{10} (y) + 3 (lo g_{10} (w) - 3 lo g_{10} (x))

7 lo g_{m} (w) - \frac{1}{3} lo g_{m} (z) + 6 lo g_{m} (x)

What is ln((10/3)/(3*3.1)) ?
The solution to ln((10/3)/(3*3.1)) is ln(10)-2ln(3)-ln(3.1)