What is 2(ln(e^5-1)-ln(e^3-1)-2) ?

The solution to 2(ln(e^5-1)-ln(e^3-1)-2) is 2(ln((e^5-1)/(e^3-1))-2)

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simplify 2(ln(e^5-1)-ln(e^3-1)-2)

simplify

2 (ln (e^{5} - 1) - ln (e^{3} - 1) - 2)

2 (ln (\frac{e ^{5} - 1}{e ^{3} - 1}) - 2)

Decimal Notation

0.08861 \dots

Solution steps

2 (ln (e^{5} - 1) - ln (e^{3} - 1) - 2)

Apply log rule:

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

ln (e^{5} - 1) - ln (e^{3} - 1) = ln (\frac{e ^{5} - 1}{e ^{3} - 1})

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

ln (\frac{e ^{4} + 2 e ^{2}}{1 + 2 e ^{2}})

5 ln (\frac{9}{8}) + 1.5 ln (\frac{13}{9}) + 3 ln (\frac{14}{13})

(ln (c (t)) - ln (c)) e^{r t}

lo g_{e} (x^{4} - 16) - 3 lo g_{e} (x - 2)

What is 2(ln(e^5-1)-ln(e^3-1)-2) ?
The solution to 2(ln(e^5-1)-ln(e^3-1)-2) is 2(ln((e^5-1)/(e^3-1))-2)