Logarithm Formulas

Posted In: Mathematics

Positive real numbers: x, y, a, c,k
Natural numbers: n

  1. $y=log_ax$ if and only if $x=a^y, a>0, a≠1$
  2. $log_a1=0$
  3. $log_aa=1$
  4. $log_a0=\{\table -∞ \if a>1;+∞ \if a<1$
  5. $log_a(xy)=log_ax+log_ay$
  6. $log_a(x/y)=log_ax-log_ay$
  7. $log_a(x^n)=log_ax^n=nlog_ax$
  8. $log_a(√^nx)=log_ax^{1/n}={1/n}log_ax$
  9. $log_ax={log_cx}/{log_ca}=log_cx.log_ac ; c>0, c≠1$
  10. $log_ac=1/{log_ca}$
  11. $a^{log_ax}=x$
  12. $log_10x=logx$, if base has not been mentioned it is base 10
  13. $log_ex=ln x$, Natural logarithm.
    where $e={lim}↙{k→∞}(1+1/k)^k$
  14. $logx=1/{ln10}lnx=0.434294$ ln x
  15. $ln x=1/{\log e}log x=2.302585$ $log x$

Post Tags: Algebra

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