Solve for x log base x of 49=2

Problem

(log_x)(49)=2

Solution

1. Identify the logarithmic equation and its base definition. The equation (log_b)(a)=c is equivalent to the exponential form bc=a

2. Rewrite the equation in exponential form by moving the base x to the other side.

(log_x)(49)=2⇒x2=49

3. Solve for x by taking the square root of both sides.

x=±√(,49)

x=±7

4. Check the constraints for the base of a logarithm. The base x must be positive (x>0 and not equal to 1 (x≠1.

5. Exclude the negative solution x=−7 because it does not satisfy the logarithmic base requirements.

x=7

Final Answer

(log_x)(49)=2⇒x=7

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