Respuesta :
The equation which is equivalent to [tex]\log _{x} 36=2[/tex] is [tex]x^{2}=36[/tex] or x = 6 ([tex]\log _{6} 36=2[/tex]).
Step-by-step explanation:
Given Equation:
[tex]\log _{x} 36=2[/tex]
As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:
[tex]b^{y}=a[/tex]
Then, the base b logarithm of x is equal to y
[tex]\log _{b}(x)=y[/tex]
Now, use the logarithmic rule for the given equation by comparing with above equation. We get b = x, y = 2, and x = 36. Apply this in equation,
[tex]b^{y}=a[/tex]
[tex]x^{2}=36[/tex]
When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as [tex]\log _{6} 36=2[/tex]
