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

Problem

(log_3)(2−x)=3

Solution

1. Identify the logarithmic equation and its base, which is 3

2. Apply the definition of a logarithm to rewrite the equation in exponential form, where (log_b)(y)=a⇔ba=y

3=2−x

3. Evaluate the exponent 3 by calculating 3⋅3⋅3

27=2−x

4. Isolate the variable x by subtracting 2 from both sides of the equation.

25=−x

5. Solve for x by multiplying or dividing both sides by −1

x=−25

6. Verify the solution by checking if the argument of the logarithm 2 - xi*s(p)*o*s(i)*t*i*v*e.S*i*n*c*e - (-25) = 27,w*h*i*c*h*i*s(g)*r*e*a*t*e*r*t*h*a*n$, the solution is valid.

Final Answer

(log_3)(2−x)=3⇒x=−25

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