Evaluate log base 36 of 1/6

Problem

(log_36)(1/6)

Solution

1. Identify the logarithmic equation by setting the expression equal to y

(log_36)(1/6)=y

2. Rewrite the equation in exponential form using the definition (log_b)(x)=y⇔by=x

36=1/6

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

(6)y=6(−1)

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

6(2*y)=6(−1)

5. Equate the exponents since the bases are the same.

2*y=−1

6. Solve for y by dividing both sides by 2

y=−1/2

Final Answer

(log_36)(1/6)=−1/2

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