Question

Find the domain and solve. For the problem please solve before the end of today.

Answer 1

Answer: Domain is All Real Numbers, x = {1, -1}

Step-by-step explanation:

log₄² (1 + x²) = 0.25        restriction: 1 + x² ≥ 0   ⇒ x² ≥ -1   ⇒ x = ARN

log₄ (1 + x²) = 0.05

       (1 + x²) = 4¹⁾²

        1 + x² = 2

             x² = 1

             x = √1

            x = +/- 1

Answer 2

Answer:

(-infinity, +infinity)

Step by-step explanation:

Here we're working with a log function.  For any base, the domain is x > 0.  If we focus on the argument of this particular log function, (1+x^2), we see that log (1+x^2) is defined for all x.  No problem if x = 0 here; the "1" in (1+x^2) takes care of that.  No problem if x grows very large; the log function can handle it.

Thus, we conclude that the domain of this function is

(-infinity, +infinity).  Never mind that this function appears as part of an equation; our job is to find the domain of the logarithmic expression on the left side of the "=" sign.