What is ln(a^n*e^{-a*(x-b)}) ?

The solution to ln(a^n*e^{-a*(x-b)}) is nln(a)-a(x-b)

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simplify ln(a^ne^{-a(x-b)})

simplify

ln (a^{n} \cdot e^{- a \cdot (x - b)})

n ln (a) - a (x - b)

Solution steps

ln (a^{n} e^{- a (x - b)})

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (a^{n}) = n ln (a)

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= n ln (a) - a (x - b) ln (e)

a (x - b) ln (e) = a (x - b)

= n ln (a) - a (x - b)

lo g_{7} (x) + \frac{1}{2} lo g_{7} (y^{6}) - 2 lo g_{7} (z)

30 \cdot ln (\frac{3}{0.2})

lo g_{10} (\frac{z ^{3}}{x ^{2} y ^{5}})

0.0259 \cdot ln (\frac{( 4.7 \cdot 1 0 ^{17} )}{1.2 \cdot 1 0 ^{18}})

- lo g_{10} (5.37 \cdot 1 0^{- 2})

What is ln(a^n*e^{-a*(x-b)}) ?
The solution to ln(a^n*e^{-a*(x-b)}) is nln(a)-a(x-b)