Question

Evaluate  log(104⋅8) .(1 point)Responseslog(104⋅8)=log(4⋅8)logarithm left parenthesis 10 superscript 4 baseline times 8 right parenthesis equals logarithm left parenthesis 4 times 8 right parenthesislog(104⋅8)=log4+8logarithm left parenthesis 10 superscript 4 baseline times 8 right parenthesis equals logarithm 4 plus 8log(104⋅8)=4+log8logarithm left parenthesis 10 superscript 4 baseline times 8 right parenthesis equals 4 plus logarithm 8log(104⋅8)=log(4+8)

Answer 1

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

The product property of logarithms states:

\[ \log(a \cdot b) = \log a + \log b \]

Applying this property, we have:

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

Next, we can evaluate \( \log(10^4) \):

\[ \log(10^4) = 4 \]

(because \( \log_{10}(10^x) = x \)).

Now we can write:

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

Thus, the evaluation is:

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

Therefore, the correct response is:

log(10^4⋅8) = 4 + log8.