Solve for x log base 3 of 3x-2=2

Problem

(log_3)(3*x−2)=2

Solution

1. Identify the logarithmic equation form (log_b)(y)=c where the base b=3 the argument y=3*x−2 and the result c=2

2. Rewrite the equation in exponential form using the definition (log_b)(y)=c⇔b^c=y

3^2=3*x−2

3. Evaluate the exponent on the left side of the equation.

9=3*x−2

4. Isolate the term containing x by adding 2 to both sides.

11=3*x

5. Solve for x by dividing both sides by 3

x=11/3

6. Verify that the solution is valid by checking if the argument of the logarithm 3*x−2 is positive.

3*(11/3)−2=11−2=9

Since 9>0 the solution is valid.

Final Answer

(log_3)(3*x−2)=2⇒x=11/3

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