Solve the equation exactly for x

[Mermaid4220]

Homework Statement

e^9x+6=8

Homework Equations

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?

 

[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}

 

[Mermaid4220]

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

 

[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.

 

[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

 

[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.

 

[Mermaid4220]

I did divide the entire thing by 9 :) but I entered it into my calculator and put the answer down because that's 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 :)

 

[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.

 

[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.

 

[Mentallic]

Mermaid, notice the confusion no brackets is causing:

Is that

e^{9x +6} = 8

or

e^{9x} + 6 = 8?

and

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}

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.