úprava logaritmu
Zdravím, je či není možné nějak upravit logaritmus [ln (e^x/x)] / [ln (e^(x+1)/(x+1)] ?
Odpovědi
Diskuze
[ln(e^x) - ln(x)] / [(x+1)ln(e) - ln(x+1)] =
[x - ln(x)] / [(x+1) - ln(x+1)]
https://www.wolframalpha.com/input/?i=simplify+%5Bx+-+ln%28x%29%5D+%2F+%5B%28x%2B1%29+-+ln%28x%2B1%29%5D
https://www.wolframalpha.com/input/?i=simplify++%5Bln+%28e%5Ex%2Fx%29%5D+%2F+%5Bln+%28e%5E%28x%2B1%29%2F%28x%2B1%29%5D
ln( e^(x+1) ) / e^x = (x+1) / e^x
muselo by to být jinak zapsané tak jak to popisuješ:
ln( e^(x+1) / e^x ) = ln( e^(x) * e^(1) / e^x ) = ln( e^(1) ) = 1