(01.02 MC)
If (8 over 2)p = 8 over 4, what is the value of p? (5 points)
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To solve this problem, we can start by simplifying the left side of the equation:
(8 over 2)p = 8 over 4
First, we simplify 8 over 2, which is equal to 4:
4p = 8 over 4
Next, we simplify 8 over 4, which is equal to 2:
4p = 2
To isolate p, we divide both sides of the equation by 4:
(4p)/4 = 2/4
This simplifies to:
p = 1/2
Therefore, the value of p is 1/2.
To solve this problem, we can start by rewriting the given equation:
(8/2)^p = 8/4
Next, we simplify both sides of the equation:
4^p = 2
Since 4 can be written as 2^2, we can rewrite the equation as follows:
(2^2)^p = 2
Using the properties of exponents, we multiply the exponents:
2^(2p) = 2
Now, we have two exponential expressions equal to each other, which means the bases must also be equal. Therefore, we can equate the exponents:
2p = 1
To solve for p, we divide both sides of the equation by 2:
p = 1/2
Therefore, the value of p is 1/2.
To find the value of p, we need to solve the equation (8/2)^p = 8/4.
First, let's simplify the fractions on both sides of the equation.
On the left side, (8/2)^p can be simplified as 4^p.
On the right side, 8/4 simplifies to 2.
So our equation becomes 4^p = 2.
To solve for p, we need to determine what power of 4 equals 2.
Taking the logarithm base 4 of both sides of the equation can help us solve for p.
log4(4^p) = log4(2)
By the power rule of logarithms, we can bring the 'p' down as a coefficient:
p * log4(4) = log4(2)
Since log4(4) equals 1, the equation simplifies to:
p = log4(2)
Now, we can use a calculator to find the value of log4(2), which is approximately 0.5.
Therefore, the value of p is 0.5.
However, none of the answer choices provided match this value. Please double-check the given answer options or the equation.