Stuck on a log equation I am having

blestimd4pz

blestimd4pz

Answered question

2022-04-03

Stuck on a log equation
I am having trouble figuring out how I can solve this log:
6log(x2+1)x=0
The steps i've thought to take so far are as follows:
step 1: subtract the right most x to the other side of the equation:
6log(x2+1)=x
step 2: divide by 6:
log(x2+1)=x6
step 3: make both sides an exponent of 10 to get rid of the log:
x2+1=10x6
step 4. ??????????????

Answer & Explanation

Ruben Gibson

Ruben Gibson

Beginner2022-04-04Added 9 answers

So
x2+1=10x6
or
x210x6+1=0
So one can use Newton's Method (i.e. choose the initial point to be x=0).
Cody Hart

Cody Hart

Beginner2022-04-05Added 11 answers

To find the biggest root, you can also iterate the equation as follows:
xn+1=6log(xn2+1)
Start for instance with x0=1.
To find the other root besides the trivial 0, you can iterate the following equation using the same seed as before:
xn+1=10xn61
Finally, you could show by an analysis of the function 6log(x2+1)x that these are the only three possible solutions.

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