Expand the expression
log2(square root of 2x/2)
square root of what ?
2x/2 = x
but
2 (sqrt 2x)/2 = sqrt (2x)
either way
log 2(square root of 2x/2) = log 2 + log (square root of Z)
= log 2 + 1/2 * log (Z)
To expand the expression log2(square root of 2x/2), we need to simplify the inside of the logarithm first.
First, let's simplify the expression inside the square root:
√(2x/2)
We can simplify this as follows:
√(2x)/√(2)
Now, let's substitute this simplified expression back into the original expression:
log2(√(2x)/√(2))
Next, let's use the property of logarithms that states logb(x/y) = logb(x) - logb(y):
log2(√(2x)) - log2(√(2))
Now, let's simplify each term further.
For the first term, log2(√(2x)), we can use the property of logarithms that states logb(sqrt(x)) = (1/2) * logb(x):
(1/2) * log2(2x) - log2(√(2))
Now, we simplify each term separately.
For the first term, (1/2) * log2(2x), notice that log2(2) is equal to 1, so:
(1/2) * (1) + log2(x)
1/2 + log2(x) - log2(√(2))
Finally, we simplify the expression:
1/2 + log2(x) - log2(√(2))