2 Answers

Siliarus · Answer 1 · 2021-07-25T07:57:55+0000

The equation which is equivalent to
$\log _(x) 36=2$ is
x^(2)=36 or x = 6 (
$\log _(6) 36=2$ ).

Explanation:

Given Equation:

$\log _(x) 36=2$

As we know, in terms of logarithmic rules, when b is raised to the power of y is equal x:

b^(y)=a

Then, the base b logarithm of x is equal to y

$\log _(b)(x)=y$

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,

b^(y)=a

x^(2)=36

When taking out the squares on both sides, we get x = 6. Hence, the given equation can be written as
$\log _(6) 36=2$

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