What is the solution to the equation 8^{(1 + | vedclass

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(C) The given equation is $8^{(1 + |\cos x| + |\cos^2 x| + |\cos^3 x| + \dots)} = 4^3$.Since the exponent is an infinite geometric series with first t

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$\pm \frac{\pi}{3}, \pm \frac{2\pi}{3}$

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(C) The given equation is $8^{(1 + |\cos x| + |\cos^2 x| + |\cos^3 x| + \dots)} = 4^3$.Since the exponent is an infinite geometric series with first term $a = 1$ and common ratio $r = |\cos x|$,where $|\cos x| Substituting this into the equation,we get $8^{\frac{1}{1 - |\cos x|}} = (2^2)^3 = 2^6 = (2^3)^2 = 8^2$.Equating the exponents,we have $\frac{1}{1 - |\cos x|} = 2$.This implies $1 - |\cos x| = \frac{1}{2}$,so $|\cos x| = 1 - \frac{1}{2} = \frac{1}{2}$.Thus,$\cos x = \pm \frac{1}{2}$.In the interval $(-\pi, \pi)$,the solutions are $x = \pm \frac{\pi}{3}$ and $x = \pm \frac{2\pi}{3}$.

What is the solution to the equation $8^{(1 + |\cos x| + |\cos^2 x| + |\cos^3 x| + \dots)} = 4^3$ in the interval $(-\pi, \pi)$?

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