# Solve the equation exactly for x

1. May 18, 2013

### Mermaid4220

1. The problem statement, all variables and given/known data
e^9x+6=8

2. Relevant equations

3. The attempt at a solution
This is what I did;
e^9x+6=8
9x+6=ln(8)
-6
9x=ln(8)-6
/9
x=ln(8)-6/9
x=1.413
My online Wiley program says it is wrong what am I doing wrong?

2. May 18, 2013

### phosgene

Is that

$e^{9x +6} = 8$

or

$e^{9x} + 6 = 8$?

Also, for your second to last step, you seem to have written

$x=ln(8) - \frac{6}{9}$

When it should be

$x=\frac{ln(8) - 6}{9}$

3. May 18, 2013

### Mermaid4220

The first one :) 9x+6 is the exponent

4. May 18, 2013

### phosgene

I think you just forgot to divide the entire right hand side by 9, instead of just dividing the 6 by 9. If you divide the entire RHS by 9, you don't get the answer that you did.

5. May 18, 2013

### Mermaid4220

I just typed in the formula and it took the formula instead of the complete answer Wiley is a weird program....I am so stumped on these...Thank you though

6. May 18, 2013

### phosgene

Do you realize what you did wrong, though? When you divide out one side by a number, you need to divide out the entire other side by the same number.

7. May 18, 2013

### Mermaid4220

I did divide the entire thing by 9 :) but I entered it into my calculator and put the answer down because thats what it asked for when it wanted just the formula for the answer :) UGH....My teacher said Logs were easier than what we were doing before...It just seems more confusing :)

8. May 18, 2013

### phosgene

It might have been because you didn't use brackets. I know that the calculator I use would interpret 'ln(8)-6/9' as

$ln(8) - \frac{6}{9}$

So for this reason, it's really important to use brackets when you're entering more than 1 term into a calculator. Other than that, you seem to be doing fine.

9. May 18, 2013

### Averki

I'm assuming that the problem asked, as is suggested in the thread title, to give solve for "x" in exact form. If you entered the decimal you found by using a calculator, the program would not recognize this because you entered an approximation. Whenever you are asked to solve for something and present the answer in exact form, you never approximate. Always keep decimals, logs, etc. in your answer when presenting your solution in exact form.

10. May 19, 2013

### Mentallic

Mermaid, notice the confusion no brackets is causing:

and

The same confusion is happening with the calculator.

a+b/c is not interpreted as $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$ but rather $a+\frac{b}{c}$. What you want to write is (a+b)/c.

Similarly, the exponent e^a+b is not interpreted as $e^{a+b}$. You want to type e^(a+b).

Always use brackets, not only for when you're posting your equations online, but when punching them into your calculator as well.