Find the Domain log base 36 of 1/6=x

Problem

(log_36)(1/6)=x

Solution

1. Identify the given equation as a logarithmic equation where the goal is to find the value of x

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(y)=x⇔bx=y

36=1/6

3. Express both sides of the equation using a common base of 6

(6)x=6(−1)

4. Apply the power of a power rule (am)n=a(m*n) to the left side of the equation.

6(2*x)=6(−1)

5. Equate the exponents since the bases are equal.

2*x=−1

6. Solve for x by dividing both sides by 2

x=−1/2

Final Answer

(log_36)(1/6)=−1/2

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