What is the first incorrect step?
Step 1: log 3^(x+1) = log15
Step 2: (x + 1)log 3 = log15
Step 3: x + 1 = log15 / log3
Step 4: x+1 = 2.708050 / 1.098612
Step 5: x + 1 = 1.418858
Step 6: x = 0.418858

Question

What is the first incorrect step?
Step 1: log 3^(x+1) = log15
Step 2: (x + 1)log 3 = log15
Step 3: x + 1 = log15 / log3
Step 4: x+1 = 2.708050 / 1.098612
Step 5: x + 1 = 1.418858
Step 6: x = 0.418858

anonymous · Answer

The first step is correct because it is rewritten as a logarithmic equation.

cathyangs · Answer

Assuming this is log (3 ^ (x+1)) = log (15)
Step 3 should be:
xlog3 + log 3 = log 15
then subtract log 3 from both sides
x log3 = log (15/3) = log 5
x = log 5 /log3

anonymous · Answer

I think the second step is correct as well because it follows the product property. All the steps look correct to me. However, the answer choices are Step 1, 2, 3, and 4.

cathyangs · Answer

I think step 3 is wrong (see above)

anonymous · Answer

YES THAT'S RIGHT!!! Thanks soo much!!

mathstudent55 · Answer

2.708050 / 1.098612 = 2.464974

mathstudent55 · Answer

If step1 is a possible answer, then was there a given equation before step 1?

anonymous · Answer

Wait isn't step 4 wrong? Log 15 doesn't equal 2.708050

mathstudent55 · Answer

The logs are natural logs.
ln 15 is equal to that number given.

anonymous · Answer

The original equation is 3^(x+1) = 15

anonymous · Answer

Ahh gotcha

mathstudent55 · Answer

Ok, I see. So taking the log is the first step.
You can take the log of any base.
That means natural logs also work.

anonymous · Answer

Do you agree step 3 is incorrect?

cathyangs · Answer

Step 5 isn't a choice for the answer to 'which step is wrong', is it? I agree with @mathstudent55 that the math doesn't work out (a la logic, 2/1 should be 2) but step 3 is a log-related mistake so I still think that's the answer.

anonymous · Answer

No the answer choices are from Steps 1-4.

anonymous · Answer

For which step is incorrect.

mathstudent55 · Answer

$3^{x+1} = 15$

$\ln 3^{x+1} = \ln 15$

$(x + 1)\ln 3 = \ln 15$

$x + 1 = \dfrac{\ln 15}{\ln 3} $

$x + 1 = \dfrac{2.708}{1.0986}$

$x = 2.46497 - 1$

$x = 1.46497$

mathstudent55 · Answer

I don't see a log related error.
I higher math where natural logs a very common, it is usual to abbreviate natural logs as log, not as ln. I see a division error, which makes this question silly.

mathstudent55 · Answer

Step 3 is correct. There is nothing wrong with it.
You can claim step 4 is wrong bec it is using log and using natural log.

anonymous · Answer

Wouldn't step 3 be correct for equal bases? This question is solving with unequal bases.

mathstudent55 · Answer

Although, as I stated above, using any base log works, and I've seen natural logs abbreviated as log many times. Perhaps in early learning of logs, you'd be stricter with log and ln, and you wouldn't call a natural log just log since you are taught that log means log base 10.
That being the case, I can see that the answer probably should be step 4.

mathstudent55 · Answer

Once again, once you agree that log means base 10, then both logs on both sides are base 10, and step 3 is correct.

mathstudent55 · Answer

Sorry, gtg. I'll be back in about 20 minutes.

anonymous · Answer

Ok thanks for your help!

cathyangs · Answer

I still disagree with @mathstudent55 and think the error is with step 3, since if you simply apply distributive property you get a different answer. I am even backed up by Wolfram Alpha, I think ( http://www.wolframalpha.com/input/?i=log+%283+%5E+%28x%2B1%29%29+%3D+log+%2815%29)

cathyangs · Answer

There's the mathematical argument for Step 3 being wrong (see above) and there's the fact that nothing is wrong going from step 3 to step 4 - so step 4 isn't wrong.

anonymous · Answer

Yeah that makes sense. I am searching my notes but I cannot find a rule or standard reason from my lesson...ughh

anonymous · Answer

I think I will go with Step 3. I will post whether it is correct or not. Thanks to both of you for you time and help!!!

cathyangs · Answer

No problem! I hope we find out what that is, I've been Google-ing XD.

anonymous · Answer

Hi I got the answer wrong. It's okay though I did well on the rest of the questions. Thanks again for sticking with me on this one!!

cathyangs · Answer

Ah, I'm sorry about that! According to Wolfram Alpha, the error is in step 3. http://www.wolframalpha.com/input/?i=log+%283+%5E+%28x%2B1%29%29+%3D+log+%2815%29 One of the "alternate forms" given is xlog3 = log 5, which follows from the application of distributive property.

anonymous · Answer

Yea no biggie...your answer makes sense.

mathstudent55 · Answer

$x + 1 = \dfrac{\log 15}{\log 3} $

$x + 1 = \dfrac{\log (3 \times 5)}{\log 3} $

$x + 1 = \dfrac{\log 3 + \log5}{\log 3} $

$x + 1 = \dfrac{\log 3}{\log 3}  + \dfrac{\log5}{\log 3} $

$x + 1 = 1  + \dfrac{\log5}{\log 3} $

$x = \dfrac{\log 5}{\log 3} $

As you can see, you can have step 3 as is given in the problem, and still arrive at the correct solution. This means step 3 is not incorrect.