1. ## One last exponent question~ Can someone check the answer, please?

With the help of the forum, I've gone through many more exponent exercises. But I have one more questions.

Problem with this one is that I do not know the answer, but I assume that the answer much be a simple whole number - all the other answers for this section are - but my solution doesn't seem to be right.

Problem

2^(x)+8*2^(-x)=9

I started out by multiplying both sides by 2^(x)... and simplified. I ended up with 20^x=18^x

any thoughts?!?

2. ## Re: One last exponent question~ Can someone check the answer, please?

Originally Posted by conpark
Problem
2^(x)+8*2^(-x)=9
I started out by multiplying both sides by 2^(x)... and simplified. I ended up with 20^x=18^x
No you don't.
You have $\displaystyle 2^{2x}+8=9\cdot 2^x$.

[TEX]2^{2x}+8=9\cdot 2^x[/TEX]

3. ## Re: One last exponent question~ Can someone check the answer, please?

Hello, conpark!

Problem with this one is that I do not know the answer. **

. . $\displaystyle 2^x+8\!\cdot\!2^{-x}\:=\:9$

Multiply by $\displaystyle 2^x\!:\;\;2^{2x} + 8 \:=\:9\!\cdot\!2^x \quad\Rightarrow\quad 2^{2x}- 9\!\cdot\!2^x + 8 \:=\:0$

Factor: .$\displaystyle \left(2^x - 1\right)\left(2^x - 8\right) \:=\:0$

Solve the resulting two equations:

. . $\displaystyle 2^x - 1 \:=\:0 \quad\Rightarrow\quad 2^x \:=\:1 \quad\Rightarrow\quad x \:=\:0$

. . $\displaystyle 2^x - 8 \:=\:0 \quad\Rightarrow\quad 2^x \:=\:8 \quad\Rightarrow\quad x \:=\:3$

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** It's difficult to solve a problem when we don't know the answer.

At the start of a trip, my odometer read 23,400 miles.
At the end of the trip, it read 23,700 miles.
I'd like to know how far I drove . . . but I don't know the answer.