If A = log_(5)2 and B= log_(5) 3, write each logarithm in terms of A and B. log_(5) 8√(3)

Question

If
`A = log_(5)2` and
`B= log_(5) 3`, write each logarithm in terms of A and B.


`log_(5) 8√(3)`

Answer 1

`A=2^{(1)/(5) }`

`B=3^{(1)/(5)}`

Explanation:

∵
`A=log_(5)2`

∴
`A^(5)=2`

∴
`A=2^{(1)/(5)}`

∵
`B=log_(5)3`

∴
`B^(5)=3`

∴
`B=3^{(1)/(5)}`