log8 2 +log8 4x^2 =2 solve

To solve the equation log8 2 + log8 4x^2 = 2, we can use the properties of logarithms.

First, we can simplify the equation using the product property of logarithms, which states that log_b (x*y) = log_b (x) + log_b (y).

So, log8 2 + log8 4x^2 can be simplified to log8 (2 * 4x^2) = 2.

We can simplify further to log8 (8x^2) = 2.

Since the base of the logarithm is 8, we can rewrite the equation as 8^(log8 (8x^2)) = 8^2.

By the definition of logarithms, 8^(log8 (8x^2)) = 8x^2.

So, the equation becomes 8x^2 = 64.

Dividing both sides by 8, we get x^2 = 8.

Taking the square root of both sides, we have x = ±√8.

Thus, the solution to the equation is x = ±√8.