To solve the given logarithmic expression [tex]\( \log_3 8 + \log_3 5 \)[/tex], we will use the properties of logarithms, specifically the property that states:
[tex]\[ \log_b(a) + \log_b(c) = \log_b(a \cdot c) \][/tex]
Here, the base [tex]\( b \)[/tex] is 3, [tex]\( a \)[/tex] is 8, and [tex]\( c \)[/tex] is 5. According to the property, we can combine the two logarithms as follows:
[tex]\[ \log_3 8 + \log_3 5 = \log_3 (8 \cdot 5) \][/tex]
Next, we calculate the product inside the logarithm:
[tex]\[ 8 \cdot 5 = 40 \][/tex]
So, our expression simplifies to:
[tex]\[ \log_3 8 + \log_3 5 = \log_3 40 \][/tex]
Thus, the question [tex]\( \log_3 8 + \log_3 5 \)[/tex] is equivalent to [tex]\( \log_3 40 \)[/tex].
The value of [tex]\( \log_3 40 \)[/tex] is approximately:
[tex]\[ \log_3 40 \approx 3.357762781432299 \][/tex]
So, the final answer is:
[tex]\[ \log_3 40 = 3.357762781432299 \][/tex]
