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Solve for x. log_(3)(2x-11)=2

Solve for x x .\newlinelog⁡3(2x−11)=2 \log _{3}(2 x-11)=2

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Full solution

Q. Solve for x x .\newlinelog⁡3(2x−11)=2 \log _{3}(2 x-11)=2
  1. Rewrite in Exponential Form: First, we need to rewrite the logarithmic equation in exponential form to isolate the term containing xx.log⁡3(2x−11)=2\log_{3}(2x - 11) = 2 is equivalent to 32=2x−113^{2} = 2x - 11
  2. Calculate Value of 323^2: Now, calculate the value of 323^2. \newline32=93^2 = 9\newlineSo, 9=2x−119 = 2x - 11
  3. Add 1111 to Both Sides: Next, we will add 1111 to both sides of the equation to isolate the term with xx on one side.9+11=2x−11+119 + 11 = 2x - 11 + 1120=2x20 = 2x
  4. Divide Both Sides by 22: Finally, we divide both sides by 22 to solve for xx.202=2x2\frac{20}{2} = \frac{2x}{2}10=x10 = x

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