Question-197147

Question Number 197147 by sonukgindia last updated on 08/Sep/23

Answered by Frix last updated on 10/Sep/23

Obviously x = 1 \lor x = \frac{π}{2} \lor x = \frac{5 π}{2} because

\ln 1 = 0 and \sin \frac{π}{2} = 1

Commented by sonukgindia last updated on 09/Sep/23

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t h i n k a l l p o s s i b i l i t i e s

Answered by MM42 last updated on 09/Sep/23

a = x^{l n (s i n x)} \Rightarrow l n a = l n x \times l n s i n x (i)

b = {(s i n x)}^{l n x} \Rightarrow l n b = l n x \times l n s i n x (i i)

(i) = (i i) \Rightarrow a = b \Rightarrow 4 a = 4 \Rightarrow a = 1

\Rightarrow l n x \times l n s i n x = 0

\Rightarrow l n x = 0 \Rightarrow \begin{matrix} x = 1 \end{matrix} ✓ o r l n s i n x = 0

\Rightarrow s i n x = 1 \Rightarrow \begin{matrix} x = 2 k π + \frac{π}{2} \end{matrix} ✓

Commented by MM42 last updated on 09/Sep/23

Commented by MathematicalUser2357 last updated on 10/Sep/23

{That}^{'} s Desmos