SOLUTION: find the value of x given 3^(x+1)+3^(2x+1)=270

Question 669212: find the value of x given 3^(x+1)+3^(2x+1)=270
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

3^x+1 + 3^2x+1 = 270

Use the principle that  on each term on the left:

3^x�3¹ + 3^2x�3¹ = 270

3^x�3 + 3^2x�3 = 270

Divide through by 3

3^x + 3^2x = 90

Rearrange the equation with 0 on the right:

3^2x + 3^x - 90 = 0

Let u = 3^x
Then u� = 3^2x

u� + u - 90 = 0

(u - 9)(u + 10) = 0

u - 9 = 0;   u + 10 = 0
    u = 9         u = -10

Using u = 9

Since u = 3^x

3^x = 9

Write 9 as 3�

3^x = 3�

Since the base 3 is the same on both
sides, is positive and not 1, we can 
equate the exponents:

x = 2

Using u = -10
Since u = 3^x

3^x = -10

Since all powers of 3 are positive,
and -10 is negative, there is no
solution to this part, and so u=-10
is extraneous.

Therefore x=2 is the only solution.

Edwin

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