Question

1. evaluate \\(\log\left(10^{4} \cdot 8\

ight)\\). (5 points)
\\(\bigcirc\\) \\(\log\left(10^{4} \cdot 8\
ight) = 4 + \log 8\\)
\\(\bigcirc\\) \\(\log\left(10^{4} \cdot 8\
ight) = \log 4 + 8\\)
\\(\bigcirc\\) \\(\log\left(10^{4} \cdot 8\
ight) = \log(4 \cdot 8)\\)
\\(\bigcirc\\) \\(\log\left(10^{4} \cdot 8\
ight) = \log(4 + 8)\\)

Explanation:

Step1: Apply log product rule

$\log(a \cdot b) = \log a + \log b$, so $\log(10^4 \cdot 8) = \log 10^4 + \log 8$

Step2: Simplify $\log 10^4$

For common log, $\log 10^x = x$, so $\log 10^4 = 4$

Step3: Combine results

Substitute to get $4 + \log 8$

Answer:

$\log(10^4 \cdot 8) = 4 + \log 8$