Question

Rewrite each expression in an equivalent form that only contains one base 10 logarithm.

log5(12500)

Answer 1

`3 + (2)/(log_(10)5)`

Explanation:

given,

log₅ (12500)

using logarithmic identity

logₐ a = 1

logₐ x³ = 3 logₐ x

log (ab) = log a + log b

logₐ x =
`(1)/(log_x a)`

now,

log₅ (12500)

log₅ (5³ × 100 )

log₅ (5³) + log₅(100)

3 log₅ (5) + log₅ (10²)

3 + 2 log₅ (10)

`3 + (2)/(log_(10)5)`

hence, the required solution is given above.