What is e^{-(ln(9)-ln(x-9))} ?

The solution to e^{-(ln(9)-ln(x-9))} is (x-9)/9

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simplify e^{-(ln(9)-ln(x-9))}

simplify

e^{- (l n (9) - l n (x - 9))}

\frac{x - 9}{9}

Solution steps

e^{- (l n (9) - l n (x - 9))}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{(l n (9) - l n (x - 9))}}

Remove parentheses:

(a) = a

= \frac{1}{e ^{l n (9) - l n (x - 9)}}

e^{l n (9) - l n (x - 9)} = \frac{9}{x - 9}

= \frac{1}{\frac{9}{x - 9}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x - 9}{9}

\frac{1}{20} x^{2} (12 x^{3})

(\frac{0. 2 ^{5}}{5}) \cdot 4 π \cdot 9 \cdot π \cdot 1 0^{- 9} \cdot \frac{1}{4}

x e^{- \frac{1}{2}}

(e^{x^{2}}) \cdot (e^{x^{- 1}})

(\frac{0. 2 ^{5}}{5}) \cdot 4 π \cdot 9 \cdot π \cdot 1 0^{- 9} \cdot \frac{1}{8}