# Formula check?

1. Apr 10, 2012

### 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??

2. Apr 10, 2012

### 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. 3.42x+3=8.5

1 or 2?

Last edited: Apr 10, 2012
3. Apr 10, 2012

### huntoon

if it is :

3.4(2x+3)=8.5

take the log of both sides.....

4. Apr 10, 2012

### Staff: Mentor

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.

5. Apr 12, 2012

### 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?

6. Apr 12, 2012

### huntoon

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!

7. Apr 12, 2012