Apparently cannot be solved using logarithms This equation clearly

FrokeFofResdts

FrokeFofResdts

Answered question

2022-03-18

Apparently cannot be solved using logarithms
This equation clearly cannot be solved using logarithms.
3+x=2(1.01x)
Now it can be solved using a graphing calculator or a computer and the answer is x=1.0202 and x=568.2993.
But is there any way to solve it algebraically/algorithmically?

Answer & Explanation

Curtiello69r

Curtiello69r

Beginner2022-03-19Added 6 answers

I have solved a question similar to this before. In general, you can have a solution of the equation
ax=bx+c
in terms of the Lambert W-function
1ln(a)Wk(1bln(a)ecln(a)b)cb
Substituting a=1.01,b=12,c=32 and considering the values k=0 and k=1, we get the zeroes
x1=1.020199952,x2=568.2993002.
Alexa Lewis

Alexa Lewis

Beginner2022-03-20Added 5 answers

Polynomials don't play nice with exponentials, so no. If you work hard, you might find an answer in terms of the Lambert W function, but if I did I wouldn't feel much more enlightened.

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