Pre-Cal Help Please: put -5e^(-4x+2)+3=(1/2)log(x^(2)+1) in simplest form

[marblefalls]

Can not figure out how to put -5e^(-4x+2)+3=(1/2)log(x^(2)+1) in simplest form. If you know how to solve this can you please explain it I do not just wan the answer I want to know how to solve this, thanks so much.

I tried condensing the log to

-5e^(-4x+2)+3=log sqrt(x^(2)+1), but I do not think that is even what one would start with and even if it was I have no idea what to do next.​

 

[Dr.Peterson]

Can not figure out how to put -5e^(-4x+2)+3=(1/2)log(x^(2)+1) in simplest form. If you know how to solve this can you please explain it I do not just wan the answer I want to know how to solve this, thanks so much.

I tried condensing the log to

-5e^(-4x+2)+3=log sqrt(x^(2)+1), but I do not think that is even what one would start with and even if it was I have no idea what to do next.​

First, we need to be sure whether log represents base 10 or something else. (It's used for whatever kind of log is most often used in a particular field, such as base 10, e, or 2.)

But in either case, I don't expect this sort of equation to be solvable by algebraic methods. I would graph it, or use a graphing calculator to find an approximate solution.

I hope you are aware that algebra can't solve every equation you can imagine; we tend to teach you only how to solve equations for which the methods we teach work, not those you can't do. In the real world, numerical solutions are usually required.

 

[mmm4444bot]

… -5 e^(-4x + 2) + 3 = (1/2) log(x^2 + 1) … how to solve this …

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This exercise seems cooked-up as something to test a student's ability to use graphing technology for finding decimal-approximated solutions (to some number of places, usually specified within the instructions), to choose appropriate viewing windows, to pay attention to detail and not miss anything. We'll need to wait for you to answer our questions -- particularly the logarithm base and instructions. :cool: