logs and exponentials

logs and exponentials

1. exponential- function in the form f(x)= ab^x

   • y=a^x aalways crosses the y xis aat1 and the x xis is n asymptote
   • y=e^x if y=e^kx then dy/dx= ke^kx

2. logarithm- this answers the question "how many of this number do we need to multiply to get this number

   • log𝑎 n=x is equivalent to a^x=n where a is not equaal to 1
   • natural logarithms are logs in the base of e Ln and e are the inverse of each other so they will cancel each other out lne^x=x e^lnx=x y=lnx alwaays crosses the x axis at 1 the y is is an asymptote
   • Laws of logarythms logx+logy=log(xy) logx-logy=log(x/y) log(x^k)=k logx log0=1
   • for equations in the form y= kx^n or y= ab^x we can take logs to transform the curves into straight lines
   • NOTE: U CANT LOG NEGATIVES

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