A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
solve5^x+1/5^1x=1/25^x
anonymous
 5 years ago
solve5^x+1/5^1x=1/25^x

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0First combine your like terms. What do you have after that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.05^x+1/5^1x = 5^x+11+x = 5^2x 1/25^x = 1/5^2x 5^2x = 1/5^2x 5^2x times 5^2x = 1 5^4x = 5^0 4x = 0 x=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't think so cause if I plug in 0 to the original equation I get: \[5^0 + 1/5^1  0 = 1/25^0\]\[\implies 1 + 1/5 = 1\]\[\implies 1 = 4/5\]\[\implies 5 = 4\] So yeah.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0did you figure this out? if not i can send you an answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no and that would be great!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok let me go slow because it take a while for me to type this in. i will do it step by step. there may be a snap way to do this but i don't see it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[5^x+\frac{1}{5}^{1x}=\frac{1}{25^x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0add the terms on the left: \[\frac{5^{x+1x}+1}{5^{1x}}=\frac{5^1+1}{5^{1x}}=\frac{6}{5^{1x}}\]\]

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Go ahead satellite :D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so we have \[\frac{6}{x^{1x}}=\frac{1}{25^x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the right hand side is \[\frac{1}{5^{2x}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{6}{5^{1x}}= \frac{1}{5^{2x}}\] \[6\times 5^{2x}=5^{1x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0take the log of both sides to get the variable out of the exponent: \[ln(6\times 5^{2x})=ln(5^{1x})\] \[ln(6) + 2xln(5) = (1x)ln(5)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now it is algebra from here on in remembering that ln(6) and ln(5) are constants.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[ln(6) +2xln(5)=ln(5)xln(5)\] \[2xln(5)+xln(5)=ln(5)ln(6)\] \[3ln(5)x=ln(5)ln(x)\] \[x=\frac{ln(5)ln(6)}{3ln(5)}\]

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Agree! :) \(5^{x}+5^{x1}=5^{2x}\) \((1+\frac{1}{5})5^x=5^{2x}\) \(\frac{6}{5}5^x=5^{2x}\) Multiply by \(5^{2x}\) we have \(\frac{6}{5}5^{3x}=1\) Then \(125^x=\frac{5}{6}\) \(x=\ln(5/6)/\ln(125)\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you choose you can rewrite this as \[\frac{ln(\frac{5}{6})}{3ln(5)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0watchman much snappier as usual. how it is going?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hrm. I woulda just: \[5^x + \frac{1}{5^{1x}} = \frac{1}{25^x}\]\[\implies 5^{x+1} + 5^x = \frac{1}{5^x}\] \[\implies 5^x(5+1) = \frac{1}{5^x} \implies 5^{2x} = \frac{1}{6}\]\[ \implies x(ln\ 25) = (ln\ 1)  (ln\ 6)\]\[\implies x = \frac{(ln\ 1)  (ln\ 6)}{(ln\ 25)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let me know if you do not understand any step

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Not sure if that's the same as what you did.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's not. Hrm.. now to see what went wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0must not be the same because we got different answers. fairly certain of mine

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1The \(5^{x+1}\) should be \(5^{x1}\) Polpak.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{1}{5}^{1x}\neq 5^{x+1}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I multiplied the whole thing by 5. \[5^x + 5^{1+x} = 5^{2x}\] \[\implies 5^{x+1} + 5^x = 5^{2x + 1}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It was the right side that I screwed up.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I canceled half the 5's from the \(1/25^x \) when I should have only cancelled one of them.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So.. \[5^{x+1} + 5^x = 5^{12x}\]\[\implies 5^x(5+1) = 5^{12x}\]\[\implies x(ln\ 5) + (ln\ 6) = (12x)(ln\ 5)\]\[\implies x = \frac{(ln\ 5)  (ln\ 6)}{3(ln\ 5)}\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.