Question

What is the value of log =" {16}^{4} " align="absmiddle" class="latex-formula">
(1 point)​

Answer 1

65,536 I believe is the answer

Answer 2

9514 1404 393

Answer:

  4·log(16) = 16·log(2) ≈ 4.81648

Step-by-step explanation:

The rules of logarithms are ...

  log(a^b) = b·log(a)

Here, we have ...

  log(16^4) = 4·log(16)

However, we recognize that 16 = 2^4, so this becomes ...

  log(16^4) = 4·(log(2^4)) = 4·4·log(2) = 16·log(2)

The base-10 logarithm of 2 is about 0.30103, so this is ...

  log(16^4) ≈ 16·0.30103 = 4.81648

Choose the form of the answer you need:

  log(16^4) = 4·log(16) = 16·log(2) ≈ 4.81648