Find the Domain log of 12(144)=y

Problem

(log_12)(144)=y

Solution

1. Identify the components of the logarithmic equation, where the base is 12 the argument is 144 and the result is y

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

3. Substitute the values into the exponential form to get the equation 12=144

4. Express the number 144 as a power of the base 12 noting that 12×12=144

5. Equate the exponents since the bases are now the same: 12=12

6. Solve for y by identifying that y=2

Final Answer

(log_12)(144)=2

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