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

Problem

(log_4)(x−3)=3

Solution

1. Identify the logarithmic equation and its base, which is 4

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

4=x−3

3. Evaluate the power 4 by calculating 4×4×4

64=x−3

4. Isolate the variable x by adding 3 to both sides of the equation.

64+3=x

x=67

5. Verify that the solution x=67 is in the domain of the logarithm by checking if x−3>0

67−3=64

64>0

Final Answer

(log_4)(x−3)=3⇒x=67

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