1. ## X Solve Check

I am solving for X below:

43x+5 = 1/256

The answer I get is -3 please correct me if I am wrong and why if you can please. Much appreciated.

2. ## Re: X Solve Check

Some brackets where they're needed would be nice.

3. ## Re: X Solve Check

I would like to learn how to do that too.

4. ## Re: X Solve Check

Well as it's written we can't tell if you meant \displaystyle \displaystyle \begin{align*} 4^{3x + 5} = \frac{1}{256} \end{align*} or \displaystyle \displaystyle \begin{align*} 4^{3x} + 5 = \frac{1}{256} \end{align*} or even \displaystyle \displaystyle \begin{align*} 4^3\,x + 5= \frac{1}{256} \end{align*}. Simply by putting what you meant to have as the power in brackets can overcome this ambiguity.

5. ## Re: X Solve Check

Im looking for the first example:

43x+5 = 1/256

Thank you, sorry for formatting.

6. ## Re: X Solve Check

From here, it's just a matter of expressing the RHS as a power of 4:

$\displaystyle \frac{1}{256}=4^{-4}$

Now, equate exponents, and solve for $\displaystyle x$.

7. ## Re: X Solve Check

Originally Posted by MarkFL2
From here, it's just a matter of expressing the RHS as a power of 4:

$\displaystyle \frac{1}{256}=4^{-4}$

Now, equate exponents, and solve for $\displaystyle x$.
Im sorry? I dont follow you.

8. ## Re: X Solve Check

Surely you know that \displaystyle \displaystyle \begin{align*} \frac{1}{256} = \frac{1}{4^4} = 4^{-4} \end{align*}.

So if \displaystyle \displaystyle \begin{align*} 4^{3x+5} = 4^{-4} \end{align*} what do you think the next step should be?

9. ## Re: X Solve Check

I'm having some trouble with this over all. I can go through it and get answers of either x = -1/3 or x = -3. Can someone help me with an example of doing it correctly. My mind is hitting the wall.

10. ## Re: X Solve Check

4^3x+5 = 1/256
-----
4^(3x+5) = 2^(8)
---
2^(6x+10) = 2^8
-----
6x + 10 = 8
6x = -2
x = -1/3

11. ## Re: X Solve Check

1/256 is 2-8 = 1/(28).

therefore, you should have:

6x + 10 = -8

try again.

12. ## Re: X Solve Check

Originally Posted by Deveno
1/256 is 2-8 = 1/(28).

therefore, you should have:

6x + 10 = -8

try again.
6x + 10 = -8

6x=-18
-- --
6 6

x=-3

13. ## Re: X Solve Check

now plug x = -3 back into your original equation....does it work?

14. ## Re: X Solve Check

I get 4^(-4) which = 1/256

So it is TRUE, correct?