formula check?

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 <<<<is this the correct way of solving and correct answer??

huntoon

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. 3.4^2x+3=8.5


1 or 2?

huntoon

if it is :

3.4^(2x+3)=8.5


take the log of both sides.....

Mark44

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

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

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

Should be:
3.4^(2x+3)=8.5

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

so....
3.4^2x * 3.4³ = 8.5

so....
3.4^2x = 8.5/3.4³

Now log both sides...
ln(3.4^2x) = 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

PLEASE USE PARENTHESES!!!!
The equation above is incorrect. It should be
(2x + 3)log3.4 = log8.5
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