What is (ln|2|-ln|1|)-(5)-(ln|4|-ln|3|) ?

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

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simplify (ln|2|-ln|1|)-(5)-(ln|4|-ln|3|)

simplify

(ln ∣ 2 ∣ - ln ∣ 1 ∣) - (5) - (ln ∣ 4 ∣ - ln ∣ 3 ∣)

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

Decimal Notation

- 4.59453 \dots

Solution steps

(ln ∣ 2 ∣ - ln ∣ 1 ∣) - (5) - (ln ∣ 4 ∣ - ln ∣ 3 ∣)

Apply log rule:

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

ln ∣ 4 ∣ - ln ∣ 3 ∣ = ln (\frac{∣ 4 ∣}{∣ 3 ∣})

= ln ∣ 2 ∣ - ln ∣ 1 ∣ - 5 - ln (\frac{∣ 4 ∣}{∣ 3 ∣})

\frac{∣ 4 ∣}{∣ 3 ∣} = \frac{4}{3}

= ln ∣ 2 ∣ - ln ∣ 1 ∣ - 5 - ln (\frac{4}{3})

Apply log rule:

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

ln ∣ 2 ∣ - ln (\frac{4}{3}) = ln (\frac{∣ 2 ∣}{\frac{4}{3}})

= ln (\frac{∣ 2 ∣}{\frac{4}{3}}) - ln ∣ 1 ∣ - 5

\frac{∣ 2 ∣}{\frac{4}{3}} = \frac{3}{2}

= ln (\frac{3}{2}) - ln ∣ 1 ∣ - 5

ln ∣ 1 ∣ = 0

= ln (\frac{3}{2}) - 0 - 5

Subtract the numbers:

- 0 - 5 = - 5

= ln (\frac{3}{2}) - 5

lo g_{10} (z x^{6})

- \frac{1}{0.00012} ln (\frac{0.211}{1})

lo g_{5} (\frac{50 w ^{7}}{2 h ^{5}})

5 ln (x - 2) + 3 ln (4) - ln (8) - 2 ln (x) - \frac{1}{2} ln (81)

\frac{\frac{423324672 \cdot 6}{( 3 - 3 )}}{ln ( 1 + 3 ) + ln ( 1 - 3 )}

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