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

The solution to (e^{ln(x)})/(e^{-ln(x))} is x^2

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

simplify

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

x^{2}

Solution steps

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

Apply exponent rule:

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

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

Apply rule

- (- a) = a

= e^{l n (x) + l n (x)}

Add similar elements:

ln (x) + ln (x) = 2 ln (x)

= e^{2 l n (x)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (e^{l n (x)})^{2}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (x)} = x

= x^{2}

\frac{( x - 2 ) ^{2}}{( x + 2 ) ^{2}}

3.64 \cdot 1 0^{- 7}

500000 \cdot e^{- 0.02 \cdot 15}

(2 x + 2)^{2} (x - 8)^{2}

What is (e^{ln(x)})/(e^{-ln(x))} ?
The solution to (e^{ln(x)})/(e^{-ln(x))} is x^2