Evaluate log(104⋅8)

Question

log
⁡
(
10
4
⋅
8
)
.(1 point)
Responses

log(104⋅8)=log(4+8)
log
⁡
(
10
4
⋅
8
)
=
log
⁡
(
4
+
8
)
the log of open paren 10 to the 4th power times 8 close paren is equal to the log of open paren 4 plus 8 close paren

log(104⋅8)=log4+8
log
⁡
(
10
4
⋅
8
)
=
log
⁡
4
+
8
the log of open paren 10 to the 4th power times 8 close paren is equal to log 4 plus 8

log(104⋅8)=4+log8
log
⁡
(
10
4
⋅
8
)
=
4
+
log
⁡
8
the log of open paren 10 to the 4th power times 8 close paren is equal to 4 plus log 8

log(104⋅8)=log(4⋅8)

Answer 1

To evaluate \( \log(10^4 \cdot 8) \), we can use the properties of logarithms. Specifically, we can use the product property of logarithms, which states that:

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

Using this property, we can break down the expression:

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

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

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

Thus, we can substitute this back into our expression:

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

Therefore, the correct evaluation is:

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

The correct answer from the options is:

log(104⋅8)=4+log8