# Thread: Find x in this equation. I know what x is, but I don't know the steps in getting it!!

1. ## Find x in this equation. I know what x is, but I don't know the steps in getting it!!

Hi all
We have our maths exam on tuesday and I am doing revision and there is a question on this sheet we have that I can't figure out the process of answering it for.

I have to find x, and I figured it out by guess + checking on the calculator, but how do I do it algebraically?
$\displaystyle 4^x+3*4^x=1$

What is the steps needed to find the answer?

Any help is appreciated
Lachlan

EDIT:
Nevermind I got it ended up being something simple which I overlooked...
I forgot that $\displaystyle 4^x+3*4^x=4*4^x$ so I understood it and divided both sides by 4, and then went from there

2. To solve this, you must use logarithms. Remember some logarithm properties

$\displaystyle \log_a{(x \cdot y)} = \log_a{x} + \log_a{y}$

$\displaystyle \log_a{\left(\frac{x}{y}\right)} = \log_a{x} - \log_a{y}$

$\displaystyle \log_a{(x)^n} = n\log_a{x}$

$\displaystyle \log_a{a} = 1$

$\displaystyle \frac{1}{a} = a^{-1}$

====================

Given: $\displaystyle 4^x + 3 * 4^x = 1$

Pull 4^x common factor: $\displaystyle 4^x(1+3) = 1$

Divide by 4 on both sides: $\displaystyle 4^x = \frac{1}{4} = 4^{-1}$

Take the log of base 4 on both sides: $\displaystyle \log_4{4^x} = \log_4{4^{-1}}$

Carry down x and -1: $\displaystyle x = -1$

Remember that $\displaystyle \log_4{4} = 1$

3. Originally Posted by auonline
I have to find x
That totally cracks me up. It's right there above the four! Where were you looking?

Seriously,

Hint: 1*y + 3*y = 4*y

4. Originally Posted by TKHunny
That totally cracks me up. It's right there above the four! Where were you looking?

Seriously,

Hint: 1*y + 3*y = 4*y
Lol, I remember that picture. "Here it is." Hehe

5. Yeah they have that picture in our classroom too:

6. Avoid Confusion: Find the value for x in the following equation...or words to that effect.

7. ## Pythagorean Theorem

Originally Posted by auonline
Yeah they have that picture in our classroom too:

Pythagoren Theorem states that in right triangle.doc

8. ## hehehe....try this one.

or try this one,...my first post was non sense, i did not your question, hehehe...
Doc3.doc