Løs for y hvis ln (y-1) = X + lny?

Svar:

# Y = 1 / (1-e ^ x) #

Forklaring:

Vi har

#ln (y-1) -ln (y) = x #

så

#ln ((y-1) / y) = x #

# (Y-1) / y = e ^ x #

# 11 / y = e ^ x #

# 1-e ^ x = 1 / y #

så

# Y = 1 / (1-e ^ x) #

Svar:

# Y = (1 / (1-e ^ x)) #

Forklaring:

Brug af logaritmen

#ln (a / b) = ln (a) -ln (b) #

#ln (y-1) -ln (y) = x #

#ln ((y-1) / y) = x #

Tag nu antilog

# ((Y-1) / y) = e ^ x #

Forenkle ovenfor ligning

# Y = (1 / (1-e ^ x)) #