Question

Please help guys :((

Answer 1

A)
`log_(5)(12)`

B)
`log_(8)(9)`

C)
`log_(9)(25)`

Explanation:

Hello! I am going to walk you through how some simple rules regarding logs!

For A, we will use the 'AM' rule! When adding logs of the same base (in this case 5), you multiply the two answers (3 and 4)!

3 · 4 = 12, giving us
`log_(5)(12)`!

For B, we will use the 'SD' rule! When subtracting logs of the same base (in this case 8), you divide the two answers (9 and 5)!

9/5 =
`(x)/(5)` ; simplify! (9/5) x 5 = 9, giving us
`log_(8)(9)`!

For C, we will use the 'MS' rule! When multiplying a number times a logarithm, you can get the same argument by removing the coefficient (2) and squaring the log's answer (5)!

`5^(2) = 25`, giving us
`log_(9)(25)`!

I hope that this helps!