What is ln((e^8-1)/(2e^4)) ?

The solution to ln((e^8-1)/(2e^4)) is ln(e^8-1)-ln(2)-4

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simplify ln((e^8-1)/(2e^4))

simplify

ln (\frac{e ^{8} - 1}{2 e ^{4}})

ln (e^{8} - 1) - ln (2) - 4

Decimal Notation

3.30651 \dots

Solution steps

ln (\frac{e ^{8} - 1}{2 e ^{4}})

Apply log rule:

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

ln (\frac{e ^{8} - 1}{2 e ^{4}}) = ln (e^{8} - 1) - ln (2 e^{4})

= ln (e^{8} - 1) - ln (2 e^{4})

Apply log rule:

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

ln (2 e^{4}) = ln (2) + ln (e^{4})

= ln (e^{8} - 1) - (ln (2) + ln (e^{4}))

Apply log rule:

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

ln (e^{4}) = 4 ln (e)

= ln (e^{8} - 1) - (ln (2) + 4 ln (e))

4 ln (e) = 4

= ln (e^{8} - 1) - (ln (2) + 4)

- (ln (2) + 4) : - ln (2) - 4

= ln (e^{8} - 1) - ln (2) - 4

ln (\frac{x}{u ^{2 n}} e^{- \frac{x ^{2}}{2 n u ^{2}}})

3 lo g_{4} (x) + lo g_{4} (y)

\frac{1}{3} ln (6) - \frac{1}{3} ln (3)

ln (\frac{901.8 + 150}{1907.2 + 150})

- lo g_{10} (4.07 \cdot 1 0^{- 5})

What is ln((e^8-1)/(2e^4)) ?
The solution to ln((e^8-1)/(2e^4)) is ln(e^8-1)-ln(2)-4