Question

Use the same numbers on the left side log(2*3)=3*log(2)+2*log(3)

Answer 1

The property that applies in this question is log(ab) = log(a) + log(b). By using this property, we can manipulate the equation and prove that it is true.

Step-by-step explanation:

The property of logarithms that applies in this question is:

log(ab) = log(a) + log(b)

Using this property, we can manipulate the equation:

log(2 * 3) = 3 * log(2) + 2 * log(3)

Breaking it down further:

1. log(2 * 3) = log(6)
2. 3 * log(2) = log(2) + log(2) + log(2) = log(2^3)
3. 2 * log(3) = log(3) + log(3) = log(3^2)

Thus, the equation becomes:

log(6) = log(2^3) + log(3^2)

And since both sides have the same base (10 in this case), we can conclude that the equation is true.