Solve for x log base 4 of x-1=3

Problem

(log_4)(x−1)=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−1

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

64=x−1

4. Isolate the variable x by adding 1 to both sides of the equation.

64+1=x

x=65

5. Verify that the solution is valid by checking if the argument of the logarithm x−1 is positive.

65−1=64

64>0

Final Answer

(log_4)(x−1)=3⇒x=65

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