how can I do this on Casio fx-85GT plus?

[batemanj]

Hello,

I need to solve 3^x = 2187 by using Casio fx-85GT plus and I couldn't find anything in its manual.

I know how to do it manually and the answer is "x = 7". But how can I do it using the calculator. Please advise, many thanks!!

I'm new to the forum, please move it to the correct section if I posted it in wrong section.



Regards,

 

[Deleted member 4993]

Hello,

I need to solve 3^x = 2187 by using Casio fx-85GT plus and I couldn't find anything in its manual.

I know how to do it manually and the answer is "x = 7". But how can I do it using the calculator. Please advise, many thanks!!

I'm new to the forum, please move it to the correct section if I posted it in wrong section.



Regards,

Take "log" of both sides and continue.

If you are still stuck, please reply back with your work from my suggestion.

 

[Dr.Peterson]

Hello,

I need to solve 3^x = 2187 by using Casio fx-85GT plus and I couldn't find anything in its manual.

I know how to do it manually and the answer is "x = 7". But how can I do it using the calculator. Please advise, many thanks!!

I'm new to the forum, please move it to the correct section if I posted it in wrong section.



Regards,

I checked your calculator's manual (see pp. 18-19), and see that it can't solve equations, but it can calculate logs with any base. Do you see how that is relevant to your question? If not, what have you learned about logarithms, or about exponential equations?

 

[batemanj]

Thanks Everyone.

Yes, the "log" did the trick which I 'm going to use. This calculator doesn't seem to have that function "directly" but I'm sure one of the scientific calculators does that as in one of the books it mentioned "using y^x button, solve it etc..."

Anyways, "log" is good enough for me to solve these,
Best regards,

 

[HallsofIvy]

Hello,

I need to solve 3^x = 2187 by using Casio fx-85GT plus and I couldn't find anything in its manual.

I know how to do it manually and the answer is "x = 7". But how can I do it using the calculator. Please advise, many thanks!!

I'm new to the forum, please move it to the correct section if I posted it in wrong section.



Regards,

You say you know how to do it "manually"- what is that method? I can see that 3^2= 9 so 3^4= (3^2)^2= 9^2= 81 while 3^3= 3(9)= 27 and then 3^7= (3^4)(3^3)= (81)(27)= 2187. Or perhaps you argued that 2187/3= 729, 729/3= 243, 243/3= 81, 81/3= 27, 27/3= 9, 9/3= 3, and 3/3= 1. That was 7 divisions by 3 so going the other way, we have to take 3 to the 7 power to get 2187. But what if the problem were to solve 3^x= 3000?
3^7= 2187 which is too small and 3^8= 6561 which is too large. x must be somewhere between 7 and 8 but where precisely? I could calculate that 3^(7.5)= 3787.99.. so that x is between 7 and 7.5 but that is stretching "manually"!

I would rather say that taking the logarithm of both sides of 3^x= 2187 I get log(3^x)= xlog(3)= log(2187) so that x= log(2187)/log(3). Your calculator has two kinds of logarithm, "common" (base 10) and "natural" (base e) but the will both give the same value for x. Using common logarithms, log(3)= 0.4771 and log(2187)= 3.3398 so x= log(2187)/log(3)= 3.3398/.4771= 7.0002. Of course both of those logarithms extend infinitely, the values here are rounded so we don't get exactly 7. Using natural logarithms, log(3)= 1.0986 and log(2187)= 7.6903 so that x= log(2187)/log(3)= 7.6903/1.0986= 7.00009, again approximately 7. It is better to "manually" calculate that 3^7= 2187

 

[Dr.Peterson]

Thanks Everyone.

Yes, the "log" did the trick which I 'm going to use. This calculator doesn't seem to have that function "directly" but I'm sure one of the scientific calculators does that as in one of the books it mentioned "using y^x button, solve it etc..."

Anyways, "log" is good enough for me to solve these,
Best regards,

I'm a little confused. What are you saying your calculator can't do? I showed you that it can do not only base 10 and base e logs, but also any base, which I would call a "direct" way to solve the equation. It is a scientific calculator. By "that function" do you mean, solving any equation you type in? That isn't what you should expect of a calculator, although in fact there are calculators that can solve an equation in some sense. But taking the log of each side is the appropriate method (not just "good enough"), so I guess you've worked that out.

 

[mmm4444bot]

… I'm sure one of the scientific calculators [solves equations because] in one of the books it mentioned "using y^x button, solve it etc..."

I don't understand why you write "one of" (above). You posted about using a Casio fx-85GT. Are you now talking about other calculators?