Solve 3^(x-2)-9=0.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

3^(x-2) - 9 = 0

To solve for x, we need to isolate x on the left side.

Let us begin by adding 9 to both sides:

==> 3^( x-2) -9 + 9 = 0 + 9

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

We will re-write 9 as 3^2

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

Now that we have equal bases, then we know that the exponents are equal.

==> (x -2) = 2

Now we will add 2 to both sides.

==> x -2 + 2 = 2 + 2

==> x = 4

Then the solution is x = 4

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve 3^(x-2) - 9 = 0.

Now we see that 9 = 3^2.

3^(x-2) - 9 = 0

=> 3^(x -2) = 9

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

As the base 3 is same on both the sides, the power should also be the same.

=> x - 2 = 2

=> x = 2+ 2

=> x = 4

Therefore the required value of x is 4.

 

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since we have 3^(x-2), we'll apply the quotient rule:

a^(b-c) = a^b/a^c

We'll put 3 = 2, b = x and c = 2

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

But 3^2  = 9

3^(x-2) = 3^x/9

We'll re-write the equation:

3^x/9  -  9 = 0

We'll multiply by 9 both sides:

3^x - 81 = 0

We'll add 81 both sides:

3^x = 81

We'll write 81 as a power of 3:

81 = 3^4

3^x = 3^4

Since the bases are matching, we'll apply one to one property:

x = 4

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

3^(x-2) -9 = 0.

To solve the equation, we recast the equation as folows:

3^(x-2) = 9.

We rewrite  the equation  replacing the 9 on the right as 3^2.

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

The bases on both sides  of the equations are same . So their exponents are also equal.

x-2 = 2.

Add 2 to both sides:

x= 2+2 = 4.

Therefore x = 4.

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