log2x2=2log2x

To solve the equation log?(x2) = 2log?(x), we can use the properties of logarithms. Let's start by rewriting the equation using the power rule of logarithms, which states that log?(bc) = clog?(b).

Applying this rule to the left side of the equation, we get:

log?(x2) = 2 log?(x)

Now, using the power rule, we can rewrite log?(x2) as 2log?(x):

2log?(x) = 2log?(x)

Since the bases are the same (both are 2), we can equate the exponents:

2 = 2

This means that the equation is true for all values of x where x > 0, because the logarithm of a negative number is undefined for real numbers.

Therefore, the solution to the equation log?(x2) = 2log?(x) is all positive real numbers, x > 0.