Question

Write the expression as a single logarithm: 2log3+log8 (Simplify your answer)

Answer 1

To combine the expression \( 2\log(3) + \log(8) \) into a single logarithm, we can use the properties of logarithms.

1. The first step involves using the power rule of logarithms, which states that \( a \log(b) = \log(b^a) \). We can rewrite \( 2\log(3) \) as:
\[
\log(3^2) = \log(9)
\]

2. Now we can rewrite the original expression:
\[
2\log(3) + \log(8) = \log(9) + \log(8)
\]

3. Next, we use the product rule of logarithms, which states that \( \log(a) + \log(b) = \log(ab) \):
\[
\log(9) + \log(8) = \log(9 \cdot 8)
\]

4. Now, calculate \( 9 \cdot 8 \):
\[
9 \cdot 8 = 72
\]

5. Thus, we have:
\[
\log(9) + \log(8) = \log(72)
\]

So, the expression \( 2\log(3) + \log(8) \) as a single logarithm is:
\[
\log(72)
\]