Verified Answer :

mpanderla95

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:

x=3.5

Step-by-step 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

\(x=\frac{7}{2} =3.5\)

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