Indice Help

[Teayarn]

Solving the equation:

3^2x - 10(3^x) + 9 = 0

What are the two solutions.
Please provide full working if possible.
Thanks

 

[Ishuda]

What have you tried? As a hint, notice that (3^x)² = 3^2x

 

[Deleted member 4993]

Solving the equation:

3^2x - 10(3^x) + 9 = 0

What are the two solutions.
Please provide full working if possible.
Thanks

Additional hint:

substitute

u = 3^x

 

[stapel]

Solving the equation:

3^2x - 10(3^x) + 9 = 0

The point of the hints provided earlier is to prod you to notice that this exponential equation is in the form of a quadratic in 3^x:

. . . . .\(\displaystyle x^2\, -\, 10x\, +\, 9\, =\, 0\)

. . . . .\(\displaystyle \left(3^x\right)^2\, -\, 10\left(3^x\right)\, +\, 9\, =\, 0\)

See the similarity? Now take the methods you learned for the first equation above, and apply them to the second equation. Then solve the two resulting (much simpler) exponential equations.