To solve this equation, we can use the properties of logarithms, specifically the addition property and the power property.
First, we can combine the logarithms on the right side of the equation using the addition property: log1/6 4 + log1/6 54 = log1/6 (4*54) = log1/6 216
Now we have the equation: 3 log1/6 x = log1/6 216
Next, we can use the power property of logarithms to rewrite the equation: log1/6 x^3 = log1/6 216
Since the logarithms are equal, the expressions inside the logarithms must be equal as well: x^3 = 216
Finally, we can solve for x by taking the cube root of both sides: x = ∛216
Therefore, x = 6.
To solve this equation, we can use the properties of logarithms, specifically the addition property and the power property.
First, we can combine the logarithms on the right side of the equation using the addition property: log1/6 4 + log1/6 54 = log1/6 (4*54) = log1/6 216
Now we have the equation: 3 log1/6 x = log1/6 216
Next, we can use the power property of logarithms to rewrite the equation: log1/6 x^3 = log1/6 216
Since the logarithms are equal, the expressions inside the logarithms must be equal as well: x^3 = 216
Finally, we can solve for x by taking the cube root of both sides: x = ∛216
Therefore, x = 6.