What is log_{e}((e^{a+b*x}-f(x))/(f(x))) ?

The solution to log_{e}((e^{a+b*x}-f(x))/(f(x))) is ln(e^{a+bx}-xf)-ln(f)-ln(x)

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simplify log_{e}((e^{a+b*x}-f(x))/(f(x)))

simplify

lo g_{e} (\frac{e ^{a + b \cdot x} - f ( x )}{f ( x )})

ln (e^{a + b x} - x f) - ln (f) - ln (x)

Solution steps

lo g_{e} (\frac{e ^{a + b x} - f ( x )}{f ( x )})

Apply log rule:

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

lo g_{e} (\frac{e ^{a + b x} - f ( x )}{f ( x )}) = lo g_{e} (e^{a + b x} - f (x)) - lo g_{e} (f (x))

= lo g_{e} (e^{b x + a} - x f) - lo g_{e} (x f)

Apply log rule:

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

lo g_{e} (f x) = lo g_{e} (f) + lo g_{e} (x)

= lo g_{e} (e^{b x + a} - x f) - (lo g_{e} (x) + lo g_{e} (f))

lo g_{e} (e^{a + b x} - f x) = ln (e^{a + b x} - x f)

- (lo g_{e} (f) + lo g_{e} (x)) = - (ln (f) + ln (x))

= ln (e^{b x + a} - x f) - (ln (x) + ln (f))

= ln (e^{a + b x} - x f) - (ln (f) + ln (x))

- (ln (f) + ln (x)) : - ln (f) - ln (x)

= ln (e^{a + b x} - f x) - ln (f) - ln (x)

= ln (e^{a + b x} - x f) - ln (f) - ln (x)

ln (\frac{y}{x ^{2 n}} \cdot e^{\frac{- m}{x}})

ln (- 2 y d y)

ln (d + w) - ln (d)

ln (\frac{1}{1 + e ^{\frac{x - y}{2}}})

10 lo g_{10} (\frac{50 \cdot 1 0 ^{- 3}}{1 \cdot 1 0 ^{- 6}})

What is log_{e}((e^{a+b*x}-f(x))/(f(x))) ?
The solution to log_{e}((e^{a+b*x}-f(x))/(f(x))) is ln(e^{a+bx}-xf)-ln(f)-ln(x)