# If 3 log 4 (a-2) = (9/2), what is a?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to find a given that 3 log 4(a-2) = 9/2.

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

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

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

take the anti log of both the sides

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

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

=> a = 8 + 2

=> a = 10

Therefore if 3 log 4(a-2) = 9/2, a = 10.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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

To find a.

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

log log4 (a-2)^3 = 9/2 , as  mlogx = logx^m.

a-2 = 4^(9/2) , as log a (b) = x  implies b = a^x.

a-2 = {4^(1/2)}^9 , as   a ^(m/n) = {a^(1/n)}^m.

a-2 = 2^9 = 512.

a = 2+512= 514.

Therefore a= 514.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll divide by 3 both sides:

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

We'll simplify and we'll get:

log4(a-2) = 3/2

Now, we'll use the property:

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

We'll put 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