What is expand e^{ln((cos(x))^{-1/2})} ?

The solution to expand e^{ln((cos(x))^{-1/2})} is 1/(cos^{1/2)(x)}

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expand e^{ln((cos(x))^{-1/2})}

expand

e^{l n ((c o s (x))^{- \frac{1}{2}})}

\frac{1}{cos ^{\frac{1}{2}} ( x )}

Solution steps

e^{l n ((c o s (x))^{- \frac{1}{2}})}

Apply log rule:

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

ln (cos^{- \frac{1}{2}} (x)) = - \frac{1}{2} ln (cos (x))

= e^{- \frac{1}{2} l n (c o s (x))}

Apply exponent rule:

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

= (e^{l n (c o s (x))})^{- \frac{1}{2}}

Apply log rule:

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

e^{l n (c o s (x))} = cos (x)

= cos^{- \frac{1}{2}} (x)

Apply exponent rule:

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

= \frac{1}{cos ^{\frac{1}{2}} ( x )}

0.0259 ln (\frac{2.8 \cdot 1 0 ^{19}}{2 \cdot 1 0 ^{16}})

ln (x^{2}) + ln (y^{0.5})

ln (\frac{1}{\frac{1}{k}})

ln (\frac{15}{17})

2 lo g_{a} (x) - 3 lo g_{a} (y) + 4 lo g_{a} (z)

What is expand e^{ln((cos(x))^{-1/2})} ?
The solution to expand e^{ln((cos(x))^{-1/2})} is 1/(cos^{1/2)(x)}