Evaluate log base 6 of 4+ log base 6 of 9

Problem

(log_6)(4)+(log_6)(9)

Solution

1. Identify the logarithmic property for addition, which states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments.

(log_b)(M)+(log_b)(N)=(log_b)(M⋅N)

2. Apply the formula to the given expression by multiplying the arguments 4 and 9 while keeping the base 6

(log_6)(4)+(log_6)(9)=(log_6)(4⋅9)

3. Simplify the product inside the logarithm.

4⋅9=36

(log_6)(36)

4. Evaluate the logarithm by determining the power to which the base 6 must be raised to obtain 36

6=36

(log_6)(36)=2

Final Answer

(log_6)(4)+(log_6)(9)=2

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