What is expand log_{(pi/2)^-}((tan(x))^{pi/2-x}) ?

The solution to expand log_{(pi/2)^-}((tan(x))^{pi/2-x}) is (pi/2-x)log_{(pi/2)^}(tan(x))

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expand log_{(pi/2)^-}((tan(x))^{pi/2-x})

expand

lo g_{(\frac{π}{2})^{-}} ((tan (x))^{\frac{π}{2} - x})

(\frac{π}{2} - x) lo g_{(\frac{π}{2})} (tan (x))

Solution steps

lo g_{(\frac{π}{2})^{-}} ((tan (x))^{\frac{π}{2} - x})

Apply log rule:

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

lo g_{(\frac{π}{2})^{-}} (tan^{\frac{π}{2} - x} (x)) = (\frac{π}{2} - x) lo g_{(\frac{π}{2})} (tan (x))

= (\frac{π}{2} - x) lo g_{(\frac{π}{2})} (tan (x))

lo g_{a} (\frac{x}{( x - y ) ^{3}}) - \frac{1}{2} (x)

ln (r^{4} s^{2} 4 r^{5} s^{2})

f (x) = 150 lo g_{e} (\frac{350}{400 - x})

ln (\frac{( x + 5 ) ^{4}}{x - 2})

ln (62)

What is expand log_{(pi/2)^-}((tan(x))^{pi/2-x}) ?
The solution to expand log_{(pi/2)^-}((tan(x))^{pi/2-x}) is (pi/2-x)log_{(pi/2)^}(tan(x))