Question

Solve for x:

log₃ (x² – 19) = 4

Answer 1

Given: log₃ (x² – 19) = 4

Step-wise calculation:

1. Convert to exponential form:

x² – 19 = 3⁴

x² – 19 = 81

2. Solve for x²: 

x² = 81 + 19

x² = 100

3. Take square roots:

x = ±10

4. Domain check: 

Require x² – 19 > 0 

⇒ x² > 19 

⇒ `|x| > sqrt(19) ≈ 4.36`

Both 10 and –10 satisfy this, so both are valid.