Question

How can I plug

4e^x=1/5

into a Ti-84 to solve?

Answer 1

\(\normalsize\color{black}{ \displaystyle 4e^x=\frac{1}{5} }\)
\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, green ,border:2px solid green ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

the steps to solve this problem by hand:

1. Divide both sides by 4,
2. Take the natural log of both sides,
\(\normalsize\color{black}{ \displaystyle ( }\)knowing the fact that \(\normalsize\color{black}{ \displaystyle \ln(e^x)~~\Rightarrow ~~ x{\tiny ~}\ln(e)~~\Rightarrow~~x. }\) \(\normalsize\color{black}{ \displaystyle ) }\)

you can plug it into mathematica as follows
\(\normalsize\color{blue}{ \displaystyle {\rm Solve}\left[4e^x==\frac{1}{5} \right] }\)
and it will solve the equation for x.

(or you can put the equation into wolframalpha (link blow).
http://www.wolframalpha.com/

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, green ,border:2px solid green ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

Sorry, but I haven't heard an option on a Ti84 (or 83) calculator to solve the equation for you just like this.

Answer 2

Note 1) In mathematica after finishing the command press Shift+Enter
Note 2) In wolfram, you have to watch out for how it will interpret the query.

Answer 3

I said link blow... it should be below.

Answer 4

Thank You!

Answer 5

Do you know how I could solve 5^x-2=24?

Answer 6

what is the exponen? x-2 ?

Answer 7

yes

Answer 8

\(\large\color{slate}{ 5^{x-2}=24 }\)

what comes to my mind is:
1) Taking log base of 5 (like \(\large\color{slate}{ \color{red}{\log_5}\left(5^{x-2}\right) = \color{red}{\log_5}(24) }\)
\(\large\color{slate}{ ( }\)Beware that the exponent will go on the outside as rule #1 says, and the \(\large\color{slate}{ \log_55 }\) that remains is equal to 1 as rule #2 says.\(\large\color{slate}{ ) }\)

2) Add 2 to both sides, after simplifying, and your x-solution is there.
\(\large\color{slate}{ ( }\)what is on the right side, can be approximated using for example http://www.wolframalpha.com/ \(\large\color{slate}{ ) }\)

\(\scriptsize\color{ slate }{\scriptsize{\bbox[5pt, royalblue ,border:2px solid royalblue ]{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ }}}\)

\(\normalsize\color{royalblue}{ \rm RULES }\)

\(\large\color{slate}{ \text{#}1 }\)

\(\Large\color{slate}{ \log_{\color{red}{a}}\left({\color{blue}{b}}^{\color{green}{c}}\right) ~~\Rightarrow~~ {\color{green}{c}}\log_{\color{red}{a}}\left({\color{blue}{b}}\right) }\)




\(\large\color{slate}{ \text{#}2 }\)

\(\Large\color{slate}{ \log_{\color{brown}{{\rm h}}}\left({\color{brown}{{\rm h}}}\right) =1}\)

provided that \(\Large\color{slate}{ {\color{brown}{{\rm h}}}>0,}\) and \(\Large\color{slate}{ {\color{brown}{{\rm h}}}\ne 1.}\)

Answer 9

if you have any questions, you can surely ask:)

Answer 10

THANK YOU SO MUCH!

Answer 11

alright.... need something else, or not right now ?

Answer 12

not right now, thank you!

Answer 13

I will post some "instructions" they might be long... and if that is a case apologize for an inconvenience.

Answer 14

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Answer 15

(the reply is showing yellow for you because you got tagged in it. Every time you are tagged in a thing (question or comment) - that is yellow. )

Answer 16

you can just have this thread on your profile for instructions, and read the post later... when you have more time (if not now).

or for reference
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