Question

we know log 32 to the base2=5.show that we get the same answer by writing 32 as 64/2 and then using the product rule . verify your answer​

Answer 1

◆ Proof -

(i) log₂32

log₂32 = log₂(2⁵)

log₂32 = 5log₂(2)

log₂32 = 5

(ii) log₂(64/2)

log₂(64/2) = log₂(64) - log₂(2)

log₂(64/2) = log₂(2⁶) - log₂(2)

log₂(64/2) = 6log₂(2) - log₂(2)

log₂(64/2) = 6 - 1

log₂(64/2) = 5

From (i) & (ii),

log₂(32) = log₂(64/2)

* Formulas used -

logₐyⁿ = nlogₐy

logₐa = 1

Hope that's useful...