Question

What is the solution to the equation 9^(x - 2) = 27 ? x = 2.5/ x = 0.5/ x = -0.5 /x = 3.5

Answer 1

To solve this question rewrite 27 as 3 to power 3. And 9 as 3 to power 2. Then distribute 2 in 3 to the power of 2 to the expression of (X-2). Cancel out 3 base at the end. Then set the equation 2x-4=3. Solving for X gives me 7/2 or 3.5.

Answer 2

x=3.5

Explanation:

`9^(x - 2) = 27`

To solve for x , we need to make same base on both sides

9 can be written as 3^2

27 can be written as 3^3

`9^(x - 2) = 27`

[tex[](3^2)^{x - 2} = 3^3[/tex]

multiply the inside exponent with inside exponent

`3^(2(x-2))= 3^3`

Both sides have same base 3

so we equation the exponents

`2(x-2)= 3`

`2x-4= 3`

add 4 on both sides

`2x=7`

divide by 2 on both sides

`x=(7)/(2) =3.5`