Maths Qn need help!! How change xe^-x = 2.46 to ln x = ax + b format??

Answer 1

x * e^(-x) = x * exp(-x) = 2.46

Take logarithm of both sides and use the following formulas:

ln(a*b) = ln(a) + ln(b)
ln(exp(z) ) = z

Thus, ln[ x * exp(-x) ] = ln(x) + (-x)
= ln(2.46)
Hnce the desired form is

ln(x) = x + ln(2.46) . Answer.

Cheers.

Answer 2

here xe^-x=2.46
so x=2.46*e^x
lnx=ln(2.46*e^x)
lnx=ln2.46+lne^x
i.e.lnx=x+ln2.46

Answer 3

note that a^x = b then log(a^x) = log(b)

and log(a^x) = x log a

xe^-x = 2.46

e^-x = 2.46*(x^-1)

log(e^-x) = log [ 2.46*(x^-1) ]

-x = log [ 2.46*(x^-1) ]

usinf =g rule : log(a*b) = log(a) + log(b)

-x = log [ 2.46] + log[(x^-1) ]

-x = log [ 2.46] + log[(x^-1) ] = log [ 2.46] + - log[x ]