What is 1-2ln|5|-3/5+ln|5-3| ?

The solution to 1-2ln|5|-3/5+ln|5-3| is ln(2/25)+2/5

Popular >

simplify 1-2ln|5|-3/5+ln|5-3|

simplify

1 - 2 ln ∣ 5 ∣ - \frac{3}{5} + ln ∣ 5 - 3 ∣

ln (\frac{2}{25}) + \frac{2}{5}

Decimal Notation

- 2.12572 \dots

Solution steps

1 - 2 ln ∣ 5 ∣ - \frac{3}{5} + ln ∣ 5 - 3 ∣

Apply log rule:

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

2 ln ∣ 5 ∣ = ln (∣ 5 ∣^{2})

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

Apply log rule:

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

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

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

\frac{∣ 5 - 3 ∣}{∣ 5 ∣ ^{2}} = \frac{2}{25}

= 1 + ln (\frac{2}{25}) - \frac{3}{5}

Combine the fractions

1 - \frac{3}{5} : \frac{2}{5}

= ln (\frac{2}{25}) + \frac{2}{5}

7 lo g_{10} (y) + 2 lo g_{10} (5 y + 3)

ln 2 - \frac{1}{2} - ln \frac{1}{6} + \frac{1}{24}

lo g_{7} (\frac{6 x}{y ^{2}})

\frac{1}{2} lo g_{10} (- 2 lo g_{10} (y))

lo g_{7} (49 x^{2})

What is 1-2ln|5|-3/5+ln|5-3| ?
The solution to 1-2ln|5|-3/5+ln|5-3| is ln(2/25)+2/5