Hi guyz.. please help me solve this...?

Question

4^x^2 = 2^x
Its four raised to the power of x^2, a bit confusing... hope you will be able to help me how to solve this one... thanks... oh here are the choices:
{0, 1/2}
{0, -4}
{0, 2}
{2, 4}

Answer 1

4^x^2 = 2^x
2^2^x^2 = 2^x
2^(4x) = 2^x

4x = x
4x - x = 0
3x = 0
x = 0

The other answer is (1/2)

ANS : {0,1/2}

Answer 2

a little test taking hint: notice how three of the 4 answers have zero as a solution? You can bet that the correct answer is one of those three. (that kind of analysis works with many algebra multiple choice questions)

substituting to make sure 4^0^2=1 and 2^0 =1

with variable exponents, you should consider solving with logarithms

I don't know if you are currently studying logarithms or not.

remember that log x^a = alog (x)

so
4^x^2=2^x
x^2log(4)=xlog(2)
x*log(4)=log(2)
x=log(2)/log(4)=1/2

Answer 3

The answer is the first choice. I hope you have a piece of paper cause I'm going to explain. The question is asking what values of X makes this equal on both sides. Seeing as how 0 appears on three choices, we can assume 0 is one of the answers. If your not sure, you can plug in zero, in which we get 1=1 on both sides. Checks out. But about the second answer. Solution: (1) We natural log both sides [ln4^X^2=ln2^X] (2) We bring the power down in front of the natural logs [X^2(ln4)=X(ln2)] (3) We isolate the X's and constants [X^2/X=(ln2)/(ln4)] (4) Now we divide and get [X=(ln2)/(ln4)] (5) Finally your answer is [X=0.5] Solved!

Answer 4

4^x² = 2^x

Get common bases. If the bases are the same, then the exponents on each side must be equal.

4 = 2², so substitute it in.

4^x² = 2^x
(2^2)^x² = 2^x

When you take a power of a power, you multiply the exponents.

2^(2x²) = 2^(x)

The bases are equal, so the exponents are, too.

2x² = x
2x² - x = 0
x(2x - 1) = 0
x = 0 or (2x - 1) = 0
2x = 1
x = 1/2

The solution is x = 0 or x = 1/2.

Answer 5

Therefore, it's 4 to the power of x times x = 2 to the power of x

The entire problem is reduced by radical x to become:

4 to the power of x = 2

Now it's a bit easier!

x = 1/2

Answer 6

I don't follow the prior answer. (edit: the first answer, the others showed up after I started typing)

2^x = (4 ^ .5) ^ x = 4 ^ (.5x)
4 ^ (X^2) = 2^x = 4 ^ (.5x)
So X^2 = .5x
Simple quadratic, x= 0 or 1/2

Answer 7

those kind of questions take hell lot of time, so i am going to easily allow you to comprehend the technique that you may do and also you may do it your self.. Take the cost of a variable,like b10, in words of b20. placed it in eq.2find b12 from lasteq and put in 2d very last. placed all values in 0.33 eqand many stuff are cancelling. each and every of the merely excellent on your exam