Solve the logarithmic equation log₂(x - 1) = 4.
Solution
Problem
Solve the logarithmic equation log₂(x - 1) = 4.
Step 1: Identify the logarithmic equation.
We are given:
log₂(x - 1) = 4
This means that the base 2 raised to the fourth power equals x - 1.
Step 2: Rewrite the equation in exponential form.
Using the relationship:
log_b(A) = c means b^c = A
we get:
2^4 = x - 1
Step 3: Evaluate the power.
2^4 = 16
So:
16 = x - 1
Step 4: Solve for x.
Add 1 to both sides:
x = 17
Step 5: Check the domain and solution.
The argument of a logarithm must be positive:
x - 1 > 0
For x = 17:
17 - 1 = 16 > 0
The solution is valid.
Therefore, x = 17.
Result
x = 17