if log2(x 2) =2log2y express x in term of y?
To express x in terms of y using the given equation:
log2(x^2) = 2log2(y)
We can use the power rule of logarithms, which states that:
logb(x^y) = y * logb(x)
Applying the power rule to the left side of the equation:
2 * log2(x) = 2log2(y)
Simplifying further:
log2(x) = log2(y)
Since both sides of the equation have the same base (log base 2), we can equate the arguments:
x = y
So, x can be expressed in terms of y as x = y.
To express x in terms of y, we'll start by using one of the logarithm rules, which states that log(base a)(b^c) = c * log(base a)(b). Applying this rule, we can rewrite the given equation:
log2(x^2) = 2 * log2(y)
Using the rule, we can simplify the equation further:
log2(x^2) = log2(y^2)
Since the logarithm function is one-to-one, we can remove the logarithm on both sides of the equation:
x^2 = y^2
Now, we can take the square root of both sides to solve for x:
√(x^2) = √(y^2)
x = ±y
So, x is equal to either positive or negative y.
since both logs are base 2, if the logs are equal, so are the numbers.
log(x^2) = 2logy = log(y^2)
x^2 = y^2
x = ±y if y > 0
assuming that x 2 means x^2
and log2y means log2y and not log 2y
If not, fix it up and then solve the adjusted equation.