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justaguide eNotes educator| Certified Educator

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

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

use the property a*log b = log b^a

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

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

=> (a - 2)^3 = 2^9

=> (a - 2)^3 = 8^3

=> a - 2 = 8

=> a = 10

The solution is a = 10

tonys538 | Student

It is given that 3log_4 (a-2) = (9/2).

The logarithm of a number a to base b is defined such that if log_b a = c, a = b^c

For 3log_4 (a-2) = (9/2)

log_4 (a-2) = (9/2)/3

log_4(a - 2) = 3/2

a - 2 = 4^(3/2)

a = 4^(3/2) + 2

a = 2^3 + 2

a = 8 + 2

a = 10

The required solution of the equation is a = 10.

giorgiana1976 | Student

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

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