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C1 exponential equations

How do you solve 9x = 3x + 2. ? It is in a C1 paper so you can't use logs.
Posted from TSR Mobile
(edited 8 years ago)
Original post by jessyjellytot14
How do you solve 9x = 3x + 2. ? It is in a C1 paper so you can't use logs.


well you know that 9=32 and that (xa)b=(xb)a 9=3^2 \ and\ that\ \left(x^a\right)^b=\left(x^b \right)^a

we also know that 3x+2=3x×32 3^{x+2}= 3^x \times 3^2
(edited 8 years ago)
Reply 3
Avatar for Nowen
Nowen
5
(3^2)^x = 3^x+2
You can use the property of injectivity: ax=ay⇒x=y if ∣a∣∉{0,1}a^x = a^y \Rightarrow x = y \text{ if } |a| \not{\in} \{0, 1\}. It uses logs implicitly though.
Reply 5
Avatar for B_9710
B_9710
18
9x=(32)x=32x 9^x=(3^2)^x=3^{2x} .
9^x is the same as 3^2x, so you get 3^2x = 3^(x+2)
From there, 2x = x+2
If you can't solve 2x = x+2, god help you, my friend.

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