How do I solve this simple math problem?

Well all you really have to do is look at this one. Try changing it to fractions;

1/2^x=1/4

One half to the what gets you a quarter? How many times do you have to multiple one half by one half to get one quarter? The answer is two because a half times a half is a quarter.


If you were going to do unnecessary work though, it would look like this.

1/2^x=1/4
x log 1/2 = log 1/4
x= log 1/4 divided by log 1/2
x=2

you can take the log of both sides or change the base of the .25 to .5
(it's .5^2)

0.25=0.5^1 XXX
0.25=0.5^2 $$$

i'm not sure what precisely you're asking. in case you may desire to simplify the 1st equation, you're able to try this by making use of factoring out the 8, wherein case you get 8*(2x - a million) that's entirely a different form of the unique given equations. For the 2d you may might desire to multiply it out, so which you have (3x-2y)(3x-2y) = 9x^2 - 6xy - 6xy + 4y^2 = 9x^2 - 12xy + 4y^2. desire this helps, yet whilst no longer, you may desire to furnish greater information with regard to the problem.

log 0.25 = x log 0.5
x = log 0.25 / log 0.5
x = 2

OR

0.5 ² = 0.5^x
x = 2

0.25 = 0.5^x
0.5^2 = 0.5^x
x = 2

There is more than one way to show this but here's an easy way.

Take logs of both sides

log(0.25) = xlog(0.5)

So x = log(0.25)/log(0.5) but 0.25 is 0.5-squared

So x = log(0.5 times 0.5)/log(0.5) =log(0.5^2)/log(0.5)

So x = 2log(0.5)/log(0.5) = 2 by cancelling.

OK?

0.25 = 0.5^x

First, change it to fractions:
1/4 = (1/2)^x

Then, change the left fraction so that it is similar to the right fraction:
(1/2)^2 = (1/2)^x

Finally, you can look at it and see that:
2 = x

I just studied this in my college algebra, kinda got the idea, but never the complete understanding...
Go to http://www-lmmb.ncifcrf.gov/~toms/paper/primer/latex/node2.htm.