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Find the value of a:  3 log 4 (a-2) = (9/2)

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Tushar Chandra eNotes educator | Certified Educator

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We have to solve 3 log 4 (a-2) = (9/2) for a

3 log(4) (a-2) = (9/2)

=> log(4) (a-2) = (9/6)

=> a - 2 = 4^(3/2)

=> a - 2 = 8

=> a = 10

The solution for the equation is a = 10

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giorgiana1976 | Student

Dividing by 3 both sides, we'll have:

log4(a-2) = 9/2*3

We'll reduce and we'll get:

log4(a-2) = 3/2

Now, we'll use the property:

log a (b) = c => b = a^c

Let a = 4, b = a-2 and c = 3/2

log4(a-2) = 3/2 <=> a - 2 = 4^(3/2)

But 4 = 2^2

a - 2 = 2^3 <=> a - 2 = 8 => a = 8 + 2 => a = 10