Question

Evaluate log(104⋅8)
.(1 point)
Responses

log(104⋅8)=log4+8
logarithm left parenthesis 10 superscript 4 baseline times 8 right parenthesis equals logarithm 4 plus 8

log(104⋅8)=4+log8
logarithm left parenthesis 10 superscript 4 baseline times 8 right parenthesis equals 4 plus logarithm 8

log(104⋅8)=log(4⋅8)
logarithm left parenthesis 10 superscript 4 baseline times 8 right parenthesis equals logarithm left parenthesis 4 times 8 right parenthesis

log(104⋅8)=log(4+8)

Answer 1

To evaluate \( \log(10^4 \cdot 8) \), we can use the properties of logarithms.

1. The property of logarithms that we'll use is:
\[
\log(a \cdot b) = \log(a) + \log(b)
\]

2. Applying this property, we have:
\[
\log(10^4 \cdot 8) = \log(10^4) + \log(8)
\]

3. We know that \( \log(10^4) = 4 \), because the logarithm of a number to its own base is the exponent.

4. Thus:
\[
\log(10^4 \cdot 8) = 4 + \log(8)
\]

Now we can match this with the provided responses. The correct evaluation is:

\[
\log(10^4 \cdot 8) = 4 + \log(8)
\]

So, the correct response is:

**log(104⋅8)=4+log8**.