Solve for x 2 log base 3 of x-3=4

Problem

2*(log_3)(x−3)=4

Solution

1. Divide both sides of the equation by 2 to isolate the logarithmic term.

(log_3)(x−3)=2

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(y)=a⇔ba=y

3=x−3

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

9=x−3

4. Solve for x by adding 3 to both sides.

x=12

5. Verify the solution by checking if the argument of the logarithm (x−3) is positive. Since 12-3 = 9,w*h*i*c*h*i*s(g)*r*e*a*t*e*r*t*h*a*n$, the solution is valid.

Final Answer

x=12

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