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: $$\log (72)$$