Question

If the expression `(3^a * 2\sqrt 9)/ (27\sqrt 4) = 1`, what is the value of a?

Answer 1

here `a=2`

Explanation:

given, `(3^a.2sqrt(9))/(27sqrt(4))=1rArr(3^a.2.3)/27.2=1rArr3^(a+1)/27=1rArr3^(a+1)=27rArr3^(a+1)=3^3rArra+1=3rArra=2`

Answer 2

`a = 2`

Explanation:

Find `a`

`(3^a⋅2√9)/(27√4) =1`

1) Find the square roots of 9 and 4

`(3^a⋅2*3)/(27*2) =1`

2) Cancel the 2 from the numerator and from the denominator
`(3^a⋅3)/(27) =1`

3) `(3^(a+1))/(27) =1`

4) Clear the fraction by multiplying both sides by 27 and letting the denominator cancel
`3^(a + 1) = 27`

5) Write 27 as `3^3`
`3^(a + 1) = 3^3`

6) The bases are both 3, so the exponents are equal
`a + 1 = 3`

7) Subtract 1 from both sides to isolate `a`
`a = 2 larr` answer

Answer:
a = 2
...................

Check
Sub in 2 for `a` in the original equation

Given `(3^a⋅2√9)/(27√4) =1`

Sub in 2
`(3^2⋅2√9)/(27√4) =1`

This is the same as
`(9*2*3)/(27*2)`
and it all should still equal 1

`(54)/(54)` does equal 1

Check!