Expert: Paul Klarreich - 4/3/2008

Question
Dear Paul,

How would I solve 1.98^2x=2 ?

I know how to set it up:

X = log 2 / 2log 1.98

But I can not seem to get the right answer.

Thanks,

Bella  

Answer
Questioner:   Bella
Category:  Advanced Math
Private:  No
 
Subject:  Log Problem
Question:  Dear Paul,

How would I solve 1.98^2x=2 ?

I know how to set it up:

X = log 2 / 2log 1.98

But I can not seem to get the right answer.

Thanks,

Bella
.................................
Hi, Bella,

I assume you meant:

1.98^(2x) = 2  

Then

ln (1.98^(2x)) = ln 2

2x ln 1.98 = ln 2
    ln 2
x = -------
   2 ln 1.98

So far so good.  
That should be about 0.5 or so.  (ln 2 is very close to ln 1.98)Now get out your trusty calculator.(in Windows, of course.)

Press:

2
ln
/
2
=
/
1.98
ln
=

That gives me 0.50735645021008734370450675626165, about 0.51.

Is that what you got?