What is the solution to the equation log₃(x) + 16 = 2?

To solve the equation log₃(x) + 16 = 2, we first isolate the logarithmic term:

1. Subtract 16 from both sides:

log3(x) = 2 - 16

This simplifies to:

log3(x) = -14

2. Now we need to convert the logarithmic form to exponential form. Recall that if log_b(a) = c, then b^c = a. Applying this principle here:

x = 3-14

This means:

x = rac{1}{314}

3. To approximate this value, we can use the fact that 3¹⁴ = 4782969. Hence:

x ≈ rac{1}{4782969}

4. Therefore, the solution to the original equation is:

x ≈ 2.09 x 10-7

In conclusion, the answer to the equation log₃(x) + 16 = 2 is:

x = 3-14 or approximately 2.09 x 10-7