Solve the equation (2^{cos x} = 8) for (x), given that (0 leq x leq 2pi).

Question

Accepted Answer

Step:1 ：Step 1: Take the natural logarithm on both sides: (ln(2^{cos x}) = ln 8).Step:2 ：Step 2: Use the property of logarithms to bring the exponent to the front: (cos x cdot ln 2 = ln 8).Step:3 ：Step 3: Note that (ln 8 = 3 ln 2), so the equation simplifies to (cos x = 3).Step:4 ：Step 4: Since the range of the cosine function is ([-1, 1]), there is no solution for this equation.

Answer

Step: 1 ：Step 1: Take the natural logarithm on both sides: (ln(2^{cos x}) = ln 8).Step: 2 ：Step 2: Use the property of logarithms to bring the exponent to the front: (cos x cdot ln 2 = ln 8).Step: 3 ：Step 3: Note that (ln 8 = 3 ln 2), so the equation simplifies to (cos x = 3).Step: 4 ：Step 4: Since the range of the cosine function is ([-1, 1]), there is no solution for this equation.

Solve the equation $2^{\cos x} = 8$ for $x$ , given that $0 \leq x \leq 2 π$ .

Answer

Popular Problems

Solve the equation 2cos⁡x=8 for x, given that 0≤x≤2π.

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Popular Problems

Solve the equation $2^{\cos x} = 8$ for $x$ , given that $0 \leq x \leq 2 π$ .