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Logarithm Properties
Properties of Logs--Precalculus
Question | Answer |
---|---|
Log\b/(x)=y ---> | b^y=x |
Log\b/(x)+Log\b/(y)= | Log\b/(xy) |
Log\b/(1)=0 | b^0=1 |
Log\b/(x^n)= | n*Log\b/(x) |
ln(x)= | ln\e/(x) |
Log\b/=(c/u) | 10(c/u)=b |
Log\3/([square root of]27)=y | 3^y=([square root of]27)= 3^y=([square root of]3^3)= 3^y=(3^3)^(1/2)=3^(3/2)--->y=3^(3/2) |
Log\4/([cubed root of]256)=y | 4^y=[cubed root of]256 |
Log parent graph? | aysmptote: y=0 ; x-int: (1,0) ; the line never touches the y-axis but increases positively and skewed right after passing through the x-axis. |
Change of base formula (for logs): Log\b/(x)= (Log\a/[x])/(Log\a/[b]) [a is any #] | Change of base formula? See if you can write it all down without looking back |
Log\8/[81]=a[any #] | (Log\a/[81])/(Log\a/[8])...say a=9 (Log\9/[81])/(Log\9/[8]) = 2/(Log\2/[8]) |