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

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

$x=\frac{7}{2} =3.5$

Answer 2

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.