## burhan101 2 years ago Solve

1. burhan101

|dw:1359089106003:dw|

2. burhan101

i can substitute 2^2 for u for all terms but the last .. idk what to do !

3. JayDS

hint: first put them all to the lowest base of 2.

4. Azteck

$\frac{ 1 }{ \sqrt{2} }=2^{-\frac{ 1 }{ 2 }}$

5. JayDS

yep, @Azteck has shown u the harder one, try to do the rest yourself. Post it on here so I/others can help u check it.

6. Azteck

@JayDS He only wanted to know the last one. Read what he said above.

7. JayDS

oh kk sorry, I didn't quite understand how he phrased it.

8. Hero

$4^2(2^{x - 3}) = 16^{x-2}$ Is that the whole thing @burhan101 ?

9. Hero

Because if it is, it works out quite nicely

10. burhan101

no @Hero you are missing the last term

11. burhan101

|dw:1359091740887:dw|

12. Hero

$4^2 \dot\ 2^{x - 3} = \frac{16^{x - 2}}{\sqrt{2}} \\4^2\dot\ 2^x2^{-3} = \frac{16^x16^{-2}}{\sqrt{2}} \\\frac{4^2 \dot\ 2^x}{2^3} = \frac{16^x}{16^2 \sqrt{2}} \\\frac{4^2 \dot\ 16^2 \sqrt{2}}{2^3}= \frac{16^x}{2^x} \\512\sqrt{2} = \left(\frac{16}{2}\right)^x \\512\sqrt{2} = \left(8\right)^x$ You should be able to finish it from there by taking logs of both sides and simplifying

13. burhan101

thank you but this is not the method my teacher wants, she wants us to substitute

14. Hero

Substitute what?

15. burhan101

like a variable like let's say use q to represent something

16. Hero

Why would she want you to do that? It simplifies quite nicely without it.

17. burhan101

I wish i knew -.- something about knowing a wide variety of methods

18. Hero

If you take logs of both sides you get: $\ln(512 \dot\ \sqrt{2}) = x \ln(8) \\\frac{\ln(512) + \ln(\sqrt{2})}{\ln(8)} = x \\\frac{\ln(2^9) + \ln(2^{1/2})}{\ln(2^3)} = x \\\frac{9\ln(2) + .5\ln(2)}{3\ln(2)} = x \\\frac{9.5 \ln(2)}{3 \ln(2)} = x \\\frac{9.5}{3} = x$

19. Azteck

$(2^2)^2(2^{2x-3})=(16^{x-2})(\frac{ 1 }{ \sqrt{2} })$ $(2^4)(2^{2x-3})=(2^{4x-8})(2^{-\frac{ 1 }{ 2 }})$ $2^{2x-3+4}=2^{4x-8-\frac{ 1 }{ 2 }}$ $2^{2x+1}=2^{4x-\frac{ 17 }{ 2 }}$ $2x+1=4x-\frac{ 17 }{ 2 }$ $4x+2=8x-17$ Solve for x.

20. Azteck

@Hero you copied the wrong indice.

21. Hero

Good job bro.