What is ln(2/(2*(1.42*10^{(-3)))}) ?

The solution to ln(2/(2*(1.42*10^{(-3)))}) is -ln(1.42)+3ln(10)

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simplify ln(2/(2(1.4210^{(-3)))})

simplify

ln (\frac{2}{2 \cdot ( 1.42 \cdot 1 0 ^{(- 3)} )})

- ln (1.42) + 3 ln (10)

Decimal Notation

6.55709 \dots

Solution steps

ln (\frac{2}{2 ( 1.42 \cdot 1 0 ^{(- 3)} )})

Apply log rule:

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

ln (\frac{2}{2 ( 1.42 \cdot 1 0 ^{(- 3)} )}) = ln (2) - ln (2 (1.42 \cdot 1 0^{(- 3)}))

= ln (2) - ln (1 0^{- 3} \cdot 2 \cdot 1.42)

Apply log rule:

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

ln (2 \cdot 1.42 \cdot 1 0^{- 3}) = ln (2) + ln (1.42) + ln (1 0^{- 3})

= ln (2) - (ln (2) + ln (1.42) + ln (1 0^{- 3}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{- 3}) = - 3 ln (10)

= ln (2) - (ln (2) + ln (1.42) - 3 ln (10))

- (ln (2) + ln (1.42) - 3 ln (10)) : - ln (2) - ln (1.42) + 3 ln (10)

= ln (2) - ln (2) - ln (1.42) + 3 ln (10)

Add similar elements:

ln (2) - ln (2) = 0

= - ln (1.42) + 3 ln (10)

ln (\frac{1}{m} e^{\frac{- ( x - 2 )}{m}})

- 6 ln (2) + \frac{15}{2} - 6 (ln (3) - ln (2)) + \frac{7}{2}

lo g_{4} (x^{2} - 11 x + 28) - lo g_{4} (x - 7)

- 3 lo g_{7} (x) + 5 lo g_{7} (y) - lo g_{3} (z)

14 + lo g_{10} (\frac{0.00084}{48})

What is ln(2/(2*(1.42*10^{(-3)))}) ?
The solution to ln(2/(2*(1.42*10^{(-3)))}) is -ln(1.42)+3ln(10)