anonymous
  • anonymous
Ciara solved the exponential equation 3x+1 = 15 and her work is shown below. What is the first step she did incorrectly? Step 1: log 3x+1 = log15 Step 2: (x + 1)log 3 = log15 Step 3: log3 = log 15 over x plus 1 Step 4: 0.477121 = 1.176091 over x plus 1 Step 5: 0.477121(x + 1) = 1.176091 Step 6: x + 1 = 1.176091 over 0.477121 Step 7: x + 1 = 2.464975 Step 8: x = 1.464975
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@Hero
Hero
  • Hero
@alexistheking777 what are your thoughts regarding this problem? Do you see which step contains the error?
anonymous
  • anonymous
I think it is either step 2 or 3?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Hero
  • Hero
By the way, if you use \(\LaTeX\) you'll be able to properly post the exponential equation. For example, you can create this: \(3^{x + 1} = 15\)
anonymous
  • anonymous
Oh okay sorry but I think it is either 2 3 or 4 2 is my first choice 4 is my second 3 is my third
Hero
  • Hero
Let's go one step at a time. We know the first step is correct because we're allowed to log both sides. What do you think is possibly wrong with the second step?
anonymous
  • anonymous
The fact that x+1 is multiplied to log 3
Hero
  • Hero
In order for any step to be wrong, we must be able to identify some mathematical rule that has been violated. Since we're using logs, then we should be able to say which rule of logs was violated for the second step. Do you know what that is (if any)?
anonymous
  • anonymous
No, I'm sorry I have a hard time with logs.
Hero
  • Hero
How familiar does the following rule look to you? \(\log(a^b) = b \log(a)\)
anonymous
  • anonymous
pretty familiar
Hero
  • Hero
Okay, now suppose \(a = 3\) and \(b = x+1\). How would using that rule of logs I posted above compare with what was done in step 2?
anonymous
  • anonymous
the x+1 can't be multiplied in step 2 because it has to be an exponent i think
anonymous
  • anonymous
@Hero
Hero
  • Hero
So for the rule \(\log(a^b) = b \log(a)\) How would you describe the role of \(b\) on the RIGHT hand side of the equation? Is \(b\) an exponent?
anonymous
  • anonymous
no not on the right side but on the left side ya
Hero
  • Hero
\(b\) is not an exponent on the right side. Correct. So in other words, according to the rule, is it possible to re-write \(\log(a^b)\) so that \(b\) is not an exponent?
anonymous
  • anonymous
Yes because it isn't on the right side
Hero
  • Hero
Okay, so knowing this, what can we say about step 2?
anonymous
  • anonymous
We can say step 2 is incorrect
anonymous
  • anonymous
Give me like 30 minutes @Hero I'll be back tho.
Hero
  • Hero
So for the rule\( log(a^b)=b \log(a)\) : b is allowed to be written as a multiple of log(a) but x+1 isn't allowed to be written as a multiple of log(3) ?
Hero
  • Hero
While you're taking a break, you should refer back to the part where I suggested for you to let \(a = 3\) and \(b = x + 1\) for the log rule I already posted.
anonymous
  • anonymous
Hey @Hero I think it can be I think x + 1 can be written as a multiple of log(3)
Hero
  • Hero
Yes, I just showed it in the drawing above.
Hero
  • Hero
You might have to zoom out to see it all.
anonymous
  • anonymous
I can't see the drawing for some reason. But with that being said it can't be one or two so I think step 4 would be incorrect. I think step 3 is right because she needed to get rid of x+1.
Hero
  • Hero
What do you mean "get rid of" x + 1? Why does she "need" to do that?
anonymous
  • anonymous
Because I think you have to do that to simplify but maybe I'm thinking of easier algebra. :(
anonymous
  • anonymous
@Hero
Hero
  • Hero
She "needs" to isolate "x". Dividing both sides by x + 1 is not a step in the direction of isolating x. Dividing both sides by x + 1 isn't getting rid of it. Instead, what it does is limit the domain of x which isn't the goal at all. I guess now you know which step is incorrect.
anonymous
  • anonymous
Thank you can you help me with a couple more if that's alright with you? Your a genius
anonymous
  • anonymous
@Hero
Hero
  • Hero
Post your next question as a new question (separate from this one). Remember anyone can help with a question.
anonymous
  • anonymous
I tagged you in the other one @Hero
Hero
  • Hero
|dw:1435362088247:dw|

Looking for something else?

Not the answer you are looking for? Search for more explanations.