Question

Which expression is equivalent to log3(x + 4)?

Answer 1

Answer:

log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.

Step-by-step explanation:

By the logarithm product rule, for two nonzero numbers $a$ and $b$,

$\log{(a \cdot b)} = \log{(a)} + \log{(b)}$.

Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.

For example, $3(x + 4)$ is the number in the logarithm $\log{[3(x + 4)]}$. Since $3(x + 4)$ is a product of the two numbers $3$ and $(x + 4)$, the logarithm $\log{[3(x + 4)]}$ can be split into two. By the logarithm product rule,

$\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}$.

However, $\log{(x + 4)}$ cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.

Answer 2

Answer:

The answer is C. on ed.

Step-by-step explanation:

log3 + log(x + 4)