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Popular >

simplify ln((e^t)/(t+1))

Solution

simplify

ln (\frac{e ^{t}}{t + 1})

Solution

t - ln (t + 1)

Solution steps

ln (\frac{e ^{t}}{t + 1})

Apply log rule:

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

ln (\frac{e ^{t}}{t + 1}) = ln (e^{t}) - ln (t + 1)

= ln (e^{t}) - ln (t + 1)

Apply log rule:

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

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

= t ln (e) - ln (t + 1)

t ln (e) = t

= t - ln (t + 1)

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Frequently Asked Questions (FAQ)

What is ln((e^t)/(t+1)) ?
The solution to ln((e^t)/(t+1)) is t-ln(t+1)