Solving for x in an Exponential Equation

[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=8.51 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

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]

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]

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 3.4^2x * 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!

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

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

x= 3-log8.5/log3.4/2
x=1.947942814?