Solve for x 2 log base 2 of x-9+ log base 2 of 2=3

Problem

2*(log_2)(x−9)+(log_2)(2)=3

Solution

1. Simplify the constant term by evaluating the logarithm (log_2)(2) which equals 1

2*(log_2)(x−9)+1=3

2. Isolate the logarithmic term by subtracting 1 from both sides of the equation.

2*(log_2)(x−9)=2

3. Divide both sides by 2 to simplify the coefficient of the logarithm.

(log_2)(x−9)=1

4. Rewrite the equation in exponential form to solve for x

x−9=2

5. Solve for x by adding 9 to both sides.

x=2+9

x=11

6. Verify the solution by checking the domain of the original logarithm; since 11−9>0 the solution is valid.

11−9=2

Final Answer

x=11

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