Solve for x 12^(x/6)=18

Problem

12(x/6)=18

Solution

1. Take the natural logarithm of both sides of the equation to isolate the exponent.

ln(12(x/6))=ln(18)

2. Apply the power rule for logarithms, which states ln(ab)=b*ln(a) to move the exponent in front of the logarithm.

x/6*ln(12)=ln(18)

3. Multiply both sides by 6 to begin isolating x

x*ln(12)=6*ln(18)

4. Divide both sides by ln(12) to solve for x

x=(6*ln(18))/ln(12)

5. Simplify the expression using the change of base formula if a single logarithm is preferred.

x=6*(log_12)(18)

Final Answer

x=(6*ln(18))/ln(12)

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