log 3​ (m 4 )=log 3​ (3 12 )

The given equation is log base 3 of m^4 equals log base 3 of 3^12.

Step 1: Understand that if log base a of b equals log base a of c, then b must equal c. This is a property of logarithms.

Step 2: Apply this property to the given equation. This means that m^4 must equal 3^12.

Step 3: To solve for m, take the fourth root of both sides of the equation. The fourth root of m^4 is m, and the fourth root of 3^12 is 3^3, because 12 divided by 4 is 3.

Step 4: Therefore, m equals 3^3, which is 27.