Solve for x log base 6 of x=-2

Problem

(log_6)(x)=−2

Solution

1. Identify the logarithmic equation in the form (log_b)(y)=a where the base b=6 the argument y=x and the exponent a=−2

2. Rewrite the equation in its equivalent exponential form using the definition of a logarithm, which states that (log_b)(y)=a is equivalent to ba=y

6(−2)=x

3. Evaluate the negative exponent by applying the rule b(−n)=1/(bn)

x=1/6

4. Simplify the denominator by calculating the square of 6.

x=1/36

Final Answer

(log_6)(x)=−2⇒x=1/36

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