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 2 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.
 2 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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brinethery
 2 years ago
Best ResponseYou've already chosen the best response.3It 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 :/

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

brinethery
 2 years ago
Best 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 :)

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

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

swarup169
 2 years ago
Best ResponseYou've already chosen the best response.1graphical 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

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

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

shfreeman
 2 years ago
Best ResponseYou've already chosen the best response.21/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 \[x \approx9.0826*10^{8}\] \[x \approx4.247\]
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