Homework Help: Exponential Eqn

1. Dec 6, 2004

aisha

To solve this exponential equation (4)(2)^5x=square root of 2
I know the common base is 2 but how do i make the square root of 2 also a common base? Do i multiply both sides by ^2? When I did this I got x=1/40 im not sure if this is the right way to do this question can someone tell me

2. Dec 6, 2004

futb0l

$$4*(\sqrt{2} * \sqrt{2})^{5x} = \sqrt{2}$$

3. Dec 6, 2004

ms. confused

I think you might be on the right track... could you explain what you did? I might have done it the way you were thinking but I got a different answer.

4. Dec 6, 2004

aisha

What I did

well first I found the common base of left side and got
(2^2) (2)^5x=square root of 2
then to get rid of the square root on the right I wasnt sure what to do but I decided to multiply both sides by ^2 and got [(2^2) (2)^5x]^2=2 so the exponents were [(2)(5x)]2 = 2 and then when i further simplified I got the exponent x to =1/40

5. Dec 6, 2004

ms. confused

When you got to here,
, what did you do with the ^2 after the 2?

6. Dec 6, 2004

aisha

I am not sure what u are talking about. :uhh:

7. Dec 6, 2004

Gokul43201

Staff Emeritus
Write both sides as powers of sqrt(2) and then compare powers.

8. Dec 6, 2004

aisha

lol sorry still confused can someone show me :uhh:

9. Dec 7, 2004

shmoe

From here "[(2^2) (2)^5x]^2=2"

to here

"so the exponents were [(2)(5x)]2 = 2"

You ran into some difficulty. The first equation is $$\left[2^{2}2^{5x}\right]^2=2$$, which is fine. When you combined the terms inside the [] you multiplied the exponents when you should have added them. You should get $$\left[2^{2+5x}\right]^2=2$$. Can you manage from here?

10. Dec 7, 2004

aisha

Ok I see my mistake but not sure if my answer is right now i got x=-1/5

11. Dec 7, 2004

Gokul43201

Staff Emeritus
No, but I think I see where you're going wrong.
Does this help (I've made a small change) ? $$\left[2^{2+5x}\right]^2=2^1$$.

12. Dec 7, 2004

shmoe

Hold on-remember the power of 2 outside the square brackets [].

It's always a good idea after solving one of these to test your solution back in the original equation.

13. Dec 7, 2004

aisha

ok this is what I am doing now the exponents are (2+5x)^2=1 this to 4+10x=1 then i get -3/10 =x

oh to check myself where do i sub in x? which part?

14. Dec 7, 2004

shmoe

Your original equation was $$4*(2)^{5x} = \sqrt{2}$$. If you replace the "x" in this equation with "-3/10", the equation should be true.

15. Dec 7, 2004

aisha

:rofl: YAYAYA
IM SOO HAPPY LOL I finally got that THANKS SO MUCH everyone ESP SHMOE