log x 8 = 2
if logx8 = 2, that means
8 = x^2
so x = √8
To solve the equation log(x) 8 = 2, we need to rewrite it in exponential form and then solve for x.
Step 1: Rewrite the equation in exponential form.
In logarithmic form, log(x) 8 = 2 means that x raised to the power of 2 is equal to 8.
So, we have x^2 = 8.
Step 2: Solve for x.
To find the value of x, we need to take the square root of both sides of the equation.
√(x^2) = √8
Since x^2 is positive (since it is squared), we can simplify the square root of x^2 to just x.
So, we have x = √8.
Now, we can simplify the square root of 8 as follows:
√8 = √(4 × 2) = √4 × √2 = 2 × √2 = 2√2.
Therefore, the solution to the equation log(x) 8 = 2 is x = 2√2.
To solve the equation log(x) 8 = 2, we need to understand the basic properties of logarithms.
The equation can be rewritten in exponential form, which will help us solve for x.
In exponential form, the equation becomes: 8 = x^2.
To find the value of x, we need to take the square root of both sides of the equation.
√8 = √(x^2)
Simplifying the equation, we get:
2√2 = x
So, the solution to the equation log(x) 8 = 2 is x = 2√2.