Question

what is \\(\log_{5}(4 \cdot 7) + \log_{5}2\\) written as a single log?

\\(\bigcirc \log_{5}21\\)
\\(\bigcirc \log_{5}26\\)
\\(\bigcirc \log_{5}30\\)
\\(\bigcirc \log_{5}56\\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Simplify the first term

Evaluate the multiplication inside the first logarithm:

$$ 4 \cdot 7 = 28 $$

So, the expression becomes:

$$ \log_{5}(28) + \log_{5}(2) $$

Step 2: Apply the product property of logarithms

Use the product rule, \(\log_{b}(x) + \log_{b}(y) = \log_{b}(x \cdot y)\), to combine the terms:

$$ \log_{5}(28 \cdot 2) $$

Step 3: Calculate the final value

Multiply the numbers inside the logarithm:

$$ 28 \cdot 2 = 56 $$

Thus, the single logarithm is:

$$ \log_{5}(56) $$

Answer:

\(\log_{5}56\)