(8^1/3) ^2 = 4^x x =

Mathematics

2 answers:

Ksju [112]3 years ago

7 0

Answer:

Step-by-step explanation:

earnstyle [38]3 years ago

4 0

Answer:

Step-by-step explanation:

This question really threw me at first, even after graphing the equation I still didn't believe the answer.

(8^1/3) ^2 = 4^x

8^2/3 = 4^x Any fractional power is a root function

x^1/2 = square of x or √x

x^ 1/3 is the is the cubic root of x or ∛x

My first thought was to multiply the 1/3 times 2 (the square).

It is more oblivious if you find the cubed of 8 and then apply the square

(∛8)² = 2² = 4 so 4 is equal to 4^x 4 = 4^x if x =1

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Solve for x, 0 ≤ x ≤2π (2cosx-1)(2sinx+√3 ) = 0

vladimir1956 [14]

Answer:

x = π/3, x = 5π/3, x = 4π/3

Step-by-step explanation:

Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.

$2\cos \left(x\right)-1=0,\\2\cos \left(x\right)=1,\\\cos \left(x\right)=\frac{1}{2}$

Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.

Similarly:

$\:2\sin \left(x\right)+\sqrt{3}=0,\\2\sin \left(x\right)=-\sqrt{3},\\\sin \left(x\right)=-\frac{\sqrt{3}}{2}$