## JJenk 2 years ago Solve. open parentheses square root of 7 close parentheses to the 6 x power = 49x-6

1. marissalovescats

2. marissalovescats

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3. JJenk

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4. marissalovescats

Hm... I recognize this. Let me go look at past notes.

5. JJenk

These were the choices i was given x = negative 21 over 2 x = -6 x = negative 6 over 5 x = -12

6. marissalovescats

Does this happen to be from a lesson called "Solve Exponential Equations" ?

7. JJenk

Yes

8. marissalovescats

Okay.. Uhm.. I've never seen one with a square root but let me see if I can solve it then I'll show you

9. Jhannybean

$\large \sqrt{(7)}^{6x}=49^{x-6}$$\large (\sqrt{7})^{6x} = \color{green}{(\sqrt{7})^{4(x-6)}}$$\large 6x = 4(x-6)$$\large 6x=4x-24$ solve for x.

10. marissalovescats

No^^^ Its not 7^4. It's 7^2.

11. marissalovescats

I got -6/5 and I'll show you.

12. marissalovescats

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13. Jhannybean

i changed it to the sae base.$$\sqrt{7}^4$$=49. and you've gotthe base $$\sqrt{7}$$ on the left side.

14. Jhannybean

Tell me how you changed $$\large (\sqrt{7})^{6x}$$ to just 7?

15. marissalovescats

I just figured because you square it. I've never done one like this. I was going out on a limb. But you are are correct because qroot7^4 is 49.

16. marissalovescats

So in that case it's -12 and not -6/5.

17. primeralph

@marissalovescats @Jhannybean Same thing.

18. primeralph

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19. marissalovescats

Yes but the way she solved it was the correct way.

20. primeralph

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21. primeralph

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22. marissalovescats

I just put 7^2 because I knew you have to have like the same "base number" Or whatever.

23. primeralph

That 's if you want to use 7 and not sqrt(7)

24. Jhannybean

$\large (\sqrt{7})^4 = 7^{4/2} = 7^2$

25. Jhannybean

Yeah....same thing.