The question is: -5e^(-4x+2) +3= 1/2log(1+x^2) Solve with a calculator for the smallest possible solution, with steps. So this hasn't really been covered in my schoolwork so I'm trying to work off what I have learned.
I started with the change of base formula because that was taught and I'm fairly certain I'm supposed to use it to solve this question because the change of base formula lesson specified "calculator". I did 1/2log(1+x^2) to log(10)sqrt(1+x^2) =p, then 10p = sqrt(1+x^2), then lnsqrt(1+x2)/ ln10.
This gave me -5e^(-4x+2) +3= .707486674 This is where I'm stuck. I haven't been taught how to solve this type of question, and my calculator won't allow it as is. Do I -3 from both sides and divide by -5? I'm still left with e-4x+2. I'm just really lost here.
Is it .6949472936?
by -3 and /-5 both sides
by taking: loge^(-4x+2)=log .4585026652
then: (-4x+2)loge= log.4585026652
then: -4xloge+2log3=log.4585026652
then -4x(loge)=log.4585026652-2loge
then -4x=-2.779789174
then divide by -4 to get .6949472936
Hmmm. I get 0.642538
I'm confused on how you got
1/2 log(1+x^2) = .707486674
in any base, since you don't know x.
How did you get .642538?
When I type it in on my graphing calc, I get .707486674. The log base is 10. I get the same result with log(sqrt[x^2+1])
I got my answer from the graphs of the functions:
http://www.wolframalpha.com/input/?i=-5e%5E(-4x%2B2)+%2B3%3D+1%2F2+log(1%2Bx%5E2)
What I don't understand is how you can evaluate log(sqrt[x^2+1]) without knowing x ...
I think when they said to use your calculator, they meant to analyze the graph. In general, if you have exponents and logs in the same equation, you can't make them both disappear.
-5e^(-4x+2)+3= log(√(1+x^2))
log(-5e^(-4x+2)+3) = log(log(√(1+x^2)))
Now you have a log of a log, and haven't gained any traction on the problem.
I am certain that I am supposed to solve the problem a certain way. The only lessons that specifically mentions calculators are the change of base lesson: Logb(A)=LogA/Logb= lnA/lnb, the common base lesson: b^M=b^N set bases equal I don't understand how my calculator is evaluating it without knowing x either, I just know that I am being given an answer.
And when I do log(log(sqrt x^2+1) I get -.150281736