Question

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

log2(800)

Answer 1

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

Explanation:

given,

log₂ (800)

using logarithmic identity

logₐ a = 1

logₐ x³ = 3 logₐ x

log (ab) = log a + log b

logₐ x =
`(1)/(log_x a)`

now,

log₂ (800)

log₂ (2³ × 100 )

log₂ (2³) + log₂ (100)

3 log₂ (2) + log₂ (10²)

3 + 2 log₂ (10)

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