What is ln((e^{2x}-1)/(2e^x)) ?

The solution to ln((e^{2x}-1)/(2e^x)) is ln(e^{2x}-1)-ln(2)-x

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simplify ln((e^{2x}-1)/(2e^x))

simplify

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

ln (e^{2 x} - 1) - ln (2) - x

Solution steps

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

Apply log rule:

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

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

= ln (e^{2 x} - 1) - ln (2 e^{x})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x ln (e) = x

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

- (ln (2) + x) : - ln (2) - x

= ln (e^{2 x} - 1) - ln (2) - x

ln (\frac{69}{119})

- ln (15 \cdot 2) + 1

ln (\frac{348}{293})

ln (7 e^{3 t - 4})

ln (\frac{0.19556}{0.1963})

What is ln((e^{2x}-1)/(2e^x)) ?
The solution to ln((e^{2x}-1)/(2e^x)) is ln(e^{2x}-1)-ln(2)-x