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## brinethery 3 years ago Solve: 64^(x – 3) = 42x I know that with most exp equations, the exponent is on one side and just a number is on the other. I'm unsure about this one since there's that x next to the 42.

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1. brinethery

It was actually someone else on here who asked this and I couldn't answer it b/c I didn't know what to do with the x on the right side :-/

2. brinethery

and I'm so nerdy that I just have to know haha

3. saifoo.khan

hold on a sec please. i will brb

4. saifoo.khan

Sorry, im back.

5. brinethery

wb

6. saifoo.khan

i know how to do this, just did this years ago. Let me recall.

7. brinethery

Lol I have the same feeling about this thing!

8. brinethery

I got as far as 64^(x-3)/42 = x and then (x-3)log(64/42) = log(x)

9. saifoo.khan

i think i found the way out, but i dont know how to write it, How can we separate 64^(x – 3) ?

10. brinethery

sec I'll look up exponential properties

11. saifoo.khan

Sure

12. brinethery
13. brinethery

so I guess... 64^x/64^3 ?

14. saifoo.khan

i will refer to my register. let me chk

15. saifoo.khan

Asked for help.

16. brinethery

If it's too much trouble then that's okay. Who knows, maybe the person who originally asked the question typed it out wrong :-?

17. brinethery

Thank you for working at it though :-)

18. saifoo.khan

Lol, it's not wrong. that's for sure.

19. brinethery

Well I've gotta go read linear algebra (which I don't want to do), so have a nice evening!

20. brinethery

I'll check back in a little bit.

21. saifoo.khan

i will send u the solution.. i want to learn this as well

22. brinethery

hahaha I've gotta stop getting people all curious!

23. brinethery

ttyl

24. saifoo.khan

Lol, that's a no problem.

25. .Sam.

I think its 64^(x – 3) = 42^x

26. brinethery

Oh damn that would make it so much easier

27. brinethery

(x-3)log(64) = xlog(42) (x-3)/x = log(42)/log(64) 1-3/x = log(42)/log(64) -x/3 = log(64)/log(42) -1 And so on and so-forth, I'm too lazy to do the rest :-)

28. swarup169

what is the level of the question i mean 2 say which class ??

29. brinethery

Another user asked it and I was curious. It's precalc level I believe.

30. swarup169

graphical solution can be applied or by taking log and then using hit and trial method or u can get the answer using scientific calculator which uses trial method for range of values provided

31. monika010191

is -1/log(64) the answer?

32. monika010191

u have taken out x common which wrong...... xln64-ln(42x) !=x(ln64-ln42)

33. shfreeman

-1/log(64) is not correct. 3 log(64) / (log(64) - log(42)) is the correct for the equation $63^{x-3}=42^{x}$ and incorrect for the equation $64^{x-3}=42x$ The truth is there is no analytic answer. There is only a numerical solution to this kind of equation (transcendental equation). Like swarup169 said you can solve it a few ways: graphically, with a good calculator, Newton's method, iteration, Taylor series,... Graphically you would plot both sides of the equation then find the x components of the intersections. By means of iteration we solve the equation for only one of the two x-s. $64^{x-3}=42x$ $x=\frac{64^{x-3}}{42}$ Then we make a guess of the answer of the original equation. For example x=1. This obviously is not the correct answer but it is probably close to it. So we plug this x1=1 into the equation and we will get a better approximation for the correct value of x. $x2=\frac{64^{x1-3}}{42}=\frac{64^{1-3}}{42}=\frac{64^{-2}}{42}=\frac{1}{42*64^{2}}\approx1.52$ Now we have x2 and again we put it back into the equation: $x3=\frac{64^{x2-3}}{42}=\frac{64^{1.52-3}}{42}=\frac{1}{42*64^{1.48}}\approx5*10^{-5}$ Keep doing this untill x does not change drastically. $x4=\frac{64^{x3-3}}{42}\approx9.1*10^{-8}$ $x5=\frac{64^{x4-3}}{42}\approx9.0826^{-8}$ Et cetera untill you have the desired accuracy. This equation actually has two real solutions. I noticed this when I plotted both sides of the equation. So to get the other solution use the same method, only solve for the x on the other side: $x=\frac{\ln(42x)}{\ln(64)}+3$ Guess the answer like x1=4. $x2=\frac{\ln(42x1)}{\ln(64)}+3\approx4.23$ $x3=\frac{\ln(42x2)}{\ln(64)}+3\approx4.25$ $x3=\frac{\ln(42x2)}{\ln(64)}+3\approx4.247$ Et cetera... So the two solutions are $x \approx9.0826*10^{-8}$ $x \approx4.247$

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