Question

positions on the Sunnyville High School Varsity Cheer Squad. The individuals will go through three weeks of training, then will be face several rounds of competition. After each round, half of the individuals will be eliminated from the try-outs.

8= answer ( answer)^x
How many rounds are needed to go from the 256 individuals trying out to the 8 individuals who will be on the Sunnyville High School Varsity Cheer Squad?

Answer 1

4^3x+5=8^4x-3 solve for x

Answer 2

By setting up the equation 256 = (8)^x, we can solve for x:

Taking the log base 8 of both sides, we get:
log8(256) = x

Now, we know that 8^2 = 64 and 8^3 = 512. Since 256 is between 64 and 512, x must be between 2 and 3.

Taking the log base 8 of 256, we get:
log8(256) = 2.5

Therefore, it will take 2.5 rounds to go from 256 individuals trying out to the 8 individuals who will be on the Sunnyville High School Varsity Cheer Squad. Since we can't have half a round, we would need at least 3 rounds to complete the process.

Answer 3

To solve the equation 4^(3x + 5) = 8^(4x - 3) for x, we will first have to rewrite 4 and 8 in terms of powers of 2.

Recall that 4 is equal to 2^2 and 8 is equal to 2^3.

Therefore, the equation becomes:

(2^2)^(3x + 5) = (2^3)^(4x - 3)

Using the properties of exponents, we can simplify this to:

2^(2(3x + 5)) = 2^(3(4x - 3))

By equating the exponents on both sides, we have:

2(3x + 5) = 3(4x - 3)

Expanding the terms, we get:

6x + 10 = 12x - 9

Rearranging terms, we have:

10 + 9 = 12x - 6x

19 = 6x

Now, divide by 6 to solve for x:

x = 19/6

Therefore, the solution for x in the given equation is x = 19/6.