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brinethery
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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.
 2 years ago
 2 years ago
brinethery Group Title
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.
 2 years ago
 2 years ago

This Question is Closed

brinethery Group TitleBest ResponseYou've already chosen the best response.3
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 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
and I'm so nerdy that I just have to know haha
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
hold on a sec please. i will brb
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
Sorry, im back.
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
i know how to do this, just did this years ago. Let me recall.
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
Lol I have the same feeling about this thing!
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
I got as far as 64^(x3)/42 = x and then (x3)log(64/42) = log(x)
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
i think i found the way out, but i dont know how to write it, How can we separate 64^(x – 3) ?
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
sec I'll look up exponential properties
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
http://www.efunda.com/math/exp_log/exp_relation.cfm
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
so I guess... 64^x/64^3 ?
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
i will refer to my register. let me chk
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
Asked for help.
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
If it's too much trouble then that's okay. Who knows, maybe the person who originally asked the question typed it out wrong :?
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
Thank you for working at it though :)
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
Lol, it's not wrong. that's for sure.
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
Well I've gotta go read linear algebra (which I don't want to do), so have a nice evening!
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
I'll check back in a little bit.
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
i will send u the solution.. i want to learn this as well
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
hahaha I've gotta stop getting people all curious!
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
Lol, that's a no problem.
 2 years ago

.Sam. Group TitleBest ResponseYou've already chosen the best response.0
I think its 64^(x – 3) = 42^x
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
Oh damn that would make it so much easier
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
(x3)log(64) = xlog(42) (x3)/x = log(42)/log(64) 13/x = log(42)/log(64) x/3 = log(64)/log(42) 1 And so on and soforth, I'm too lazy to do the rest :)
 2 years ago

swarup169 Group TitleBest ResponseYou've already chosen the best response.1
what is the level of the question i mean 2 say which class ??
 2 years ago

brinethery Group TitleBest ResponseYou've already chosen the best response.3
Another user asked it and I was curious. It's precalc level I believe.
 2 years ago

swarup169 Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

monika010191 Group TitleBest ResponseYou've already chosen the best response.0
is 1/log(64) the answer?
 2 years ago

monika010191 Group TitleBest ResponseYou've already chosen the best response.0
u have taken out x common which wrong...... xln64ln(42x) !=x(ln64ln42)
 2 years ago

shfreeman Group TitleBest ResponseYou've already chosen the best response.2
1/log(64) is not correct. 3 log(64) / (log(64)  log(42)) is the correct for the equation \[63^{x3}=42^{x}\] and incorrect for the equation \[64^{x3}=42x\] 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 xs. \[64^{x3}=42x\] \[x=\frac{64^{x3}}{42}\] 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. \[x2=\frac{64^{x13}}{42}=\frac{64^{13}}{42}=\frac{64^{2}}{42}=\frac{1}{42*64^{2}}\approx1.52\] Now we have x2 and again we put it back into the equation: \[x3=\frac{64^{x23}}{42}=\frac{64^{1.523}}{42}=\frac{1}{42*64^{1.48}}\approx5*10^{5}\] Keep doing this untill x does not change drastically. \[x4=\frac{64^{x33}}{42}\approx9.1*10^{8}\] \[x5=\frac{64^{x43}}{42}\approx9.0826^{8}\] 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 \[x \approx9.0826*10^{8}\] \[x \approx4.247\]
 2 years ago
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