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Formula check? 
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#1
Apr1012, 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?? 


#2
Apr1012, 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. 3.4^{2x}+3=8.5 1 or 2? 


#3
Apr1012, 12:21 PM

P: 145

if it is :
3.4^{(2x+3)}=8.5 take the log of both sides..... 


#4
Apr1012, 12:23 PM

Mentor
P: 21,249

Formula check?
There is even a third possibility:
3.4^{2}x + 3 = 8.5 


#5
Apr1212, 03:32 AM

P: 6

3.4^(2x+3)=8.5 2x+3log3.4=log8.5 2x=3log8.5/log3.4 x= 3log8.5/log3.4/2 x=1.947942814? 


#6
Apr1212, 04:37 AM

P: 145

3.4^{(2x+3)}=8.5 exponent rule first: 3.4^{(2x+3)} becomes 3.4^{2x} * 3.4^{3} so.... 3.4^{2x} * 3.4^{3} = 8.5 so.... 3.4^{2x} = 8.5/3.4^{3} Now log both sides... ln(3.4^{2x}) = ln(8.5/3.4^{3}) apply log rule: 2xln(3.4) = ln(8.5/3.4^{3}) therefore: x = ln(8.5/3.4^{3})/(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! 


#7
Apr1212, 12:42 PM

Mentor
P: 21,249

PLEASE USE PARENTHESES!!!!
(2x + 3)log3.4 = log8.5 Starting from (2x + 3)log3.4 = log8.5 there is no way you can get to 2x=3log8.5/log3.4 


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