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Formula check?

by steveandy2002
Tags: check, formula
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steveandy2002
#1
Apr10-12, 08:38 AM
P: 6
I need to find x from (3.4)^2x+3=8.5
what i have done is as follows
3.4^2x = 11.56
3.4^2x+3 = 14.56
8.5 - 14.56 = x
x=-6.06 <<<<is this the correct way of solving and correct answer??
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huntoon
#2
Apr10-12, 11:02 AM
P: 145
Hi SteveAndy
Your formula is a bit confusing:

(3.4)^2x+3=8.5

Should the formula look like this:

1. 3.4(2x+3)=8.5

or

2. 3.42x+3=8.5


1 or 2?
huntoon
#3
Apr10-12, 12:21 PM
P: 145
if it is :

3.4(2x+3)=8.5


take the log of both sides.....

Mark44
#4
Apr10-12, 12:23 PM
Mentor
P: 21,215
Formula check?

There is even a third possibility:
3.42x + 3 = 8.5

Quote Quote by steveandy2002
I need to find x from (3.4)^2x+3=8.5
what i have done is as follows
3.4^2x = 11.56
3.4^2x+3 = 14.56
8.5 - 14.56 = x
x=-6.06
Putting aside the uncertainty of what the original equation actually is, how did you go from the first equation to the second? The 11.56 in the second equation happens to be 3.42, but the second equation should not involve x.
steveandy2002
#5
Apr12-12, 03:32 AM
P: 6
Quote Quote by huntoon View Post
if it is :

3.4(2x+3)=8.5


take the log of both sides.....
so based on useing logs would the folllowing be correct??
3.4^(2x+3)=8.5
2x+3log3.4=log8.5
2x=3-log8.5/log3.4
x= 3-log8.5/log3.4/2
x=1.947942814?
huntoon
#6
Apr12-12, 04:37 AM
P: 145
Quote Quote by steveandy2002 View Post
so based on useing logs would the folllowing be correct??
3.4^(2x+3)=8.5
2x+3log3.4=log8.5
2x=3-log8.5/log3.4
x= 3-log8.5/log3.4/2
x=1.947942814?
Should be:
3.4(2x+3)=8.5

exponent rule first:
3.4(2x+3) becomes 3.42x * 3.43

so....
3.42x * 3.43 = 8.5

so....
3.42x = 8.5/3.43

Now log both sides...
ln(3.42x) = ln(8.5/3.43)

apply log rule:
2xln(3.4) = ln(8.5/3.43)

therefore:
x = ln(8.5/3.43)/(2ln(3.4))

I get approx: -0.63 for x.


and to check:

3.4(2(-0.63)+3)=8.5
3.4(1.74)=8.5
8.4 = 8.5

hmm... too much rounding, but close enough!
Mark44
#7
Apr12-12, 12:42 PM
Mentor
P: 21,215
PLEASE USE PARENTHESES!!!!
Quote Quote by steveandy2002 View Post
so based on useing logs would the folllowing be correct??
3.4^(2x+3)=8.5
2x+3log3.4=log8.5
The equation above is incorrect. It should be
(2x + 3)log3.4 = log8.5
Quote Quote by steveandy2002 View Post
2x=3-log8.5/log3.4
This is wrong as well.
Starting from (2x + 3)log3.4 = log8.5 there is no way you can get to 2x=3-log8.5/log3.4
Quote Quote by steveandy2002 View Post
x= 3-log8.5/log3.4/2
x=1.947942814?


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