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