# Formula check?

by steveandy2002
Tags: check, formula
 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 <<<
 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?
 P: 145 if it is : 3.4(2x+3)=8.5 take the log of both sides.....
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Formula check?

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

 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.
P: 6
 Quote by huntoon 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?
P: 145
 Quote by 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?
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!
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