To solve this equation, we will first apply the properties of logarithms to combine the terms on the right side of the equation:
log^23x - log^24 - log^2*6 = 0
Now, we can combine the logarithms using the property that states log(a) - log(b) = log(a/b):
log^2(3x / 4 6) = 0
Now, we simplify the expression in parentheses:
3x / (4 * 6) = 3x / 24 = x / 8
So, the equation becomes:
log^2*(x / 8) = 0
Since the base of the logarithm is not specified, we assume it is 10. Therefore, we can rewrite the equation as:
log(x / 8) = 0
Now, using the definition of logarithms, we can rewrite the equation as:
x / 8 = 10^0
x / 8 = 1
Multiplying both sides by 8, we get:
x = 8
Therefore, the solution to the equation is x = 8.
To solve this equation, we will first apply the properties of logarithms to combine the terms on the right side of the equation:
log^23x - log^24 - log^2*6 = 0
Now, we can combine the logarithms using the property that states log(a) - log(b) = log(a/b):
log^2(3x / 4 6) = 0
Now, we simplify the expression in parentheses:
3x / (4 * 6) = 3x / 24 = x / 8
So, the equation becomes:
log^2*(x / 8) = 0
Since the base of the logarithm is not specified, we assume it is 10. Therefore, we can rewrite the equation as:
log(x / 8) = 0
Now, using the definition of logarithms, we can rewrite the equation as:
x / 8 = 10^0
x / 8 = 1
Multiplying both sides by 8, we get:
x = 8
Therefore, the solution to the equation is x = 8.