3logx2+logx18=2

The given equation is 3log(x^2) + log(x^18) = 2.

Step 1: Apply the power rule of logarithms, which states that log(a^b) = b*log(a).

This gives us 32log(x) + 18*log(x) = 2.

Step 2: Simplify the equation.

This gives us 6log(x) + 18log(x) = 2.

Step 3: Combine like terms.

This gives us 24*log(x) = 2.

Step 4: Divide both sides by 24.

This gives us log(x) = 2/24 = 1/12.

Step 5: To solve for x, we need to rewrite the equation in exponential form.

This gives us x = 10^(1/12).

So, the solution to the equation is x = 10^(1/12).