What is ln((2t)/(t^4+2t+1)) ?

The solution to ln((2t)/(t^4+2t+1)) is ln(2)+ln(t)-ln(t^4+2t+1)

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simplify ln((2t)/(t^4+2t+1))

simplify

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

ln (2) + ln (t) - ln (t^{4} + 2 t + 1)

Solution steps

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

Apply log rule:

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

ln (\frac{2 t}{t ^{4} + 2 t + 1}) = ln (2 t) - ln (t^{4} + 2 t + 1)

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

Apply log rule:

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

ln (2 t) = ln (2) + ln (t)

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

ln (8) + 5 ln (x) + 5 ln (x^{2} + 7)

ln (\frac{N}{N o})

ln (3.8) + ln (9.4)

ln (\frac{66}{78})

ln (a) - 3 ln (b) + 5 ln (c)

What is ln((2t)/(t^4+2t+1)) ?
The solution to ln((2t)/(t^4+2t+1)) is ln(2)+ln(t)-ln(t^4+2t+1)