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Properties of Logarithms
1. logb1 = 0 . It follows from the fact that bo = 1.
2. logb b = 1. It follows from the fact that b 1= b .
3. logb bx = x . it can be generalized out to blog b f ( x ) = f ( x ).
4. b logb x = x . It can be generalized out to b logb f ( x ) = f ( x ) .
Properties 3 and 4 lead to a pleasant relationship among the logarithm & exponential function.
Let's first calculate the following function compositions for f ( x )= b x and g ( x ) = logb x .
( f o g )( x ) = f [g ( x )] = f (logb x ) = b logb x = x
( g o f ) ( x ) = g [f ( x )]= g [b x ] = log b bx = x
Remember again from the section on inverse functions which this means that the exponential & logarithm functions are inverses of each other. It is a nice fact to remember on occasion.
We have to also give the generalized version of Properties 3 & 4 in terms of both the natural and common logarithm
ln e f ( x ) = f ( x) log10 f ( x ) = f ( x)
eln f ( x ) = f ( x ) 10log f ( x ) = f ( x )
r-17
how do I do it?
y=2x 2x
if I have the equation 3(x+4y)+5(2x-y)an then I change it into (3x+12y)+(10x-5y) what property is it
2a*2b
Solve (3x+ 1/ x + 4 ) ≥ 1. Solution The first thing that we have to do here is subtract 1 from both of sides and then get everything in a single rational expression. (3
a long distance telephone company charges 7 cents per minute or a 50 cent minimum charge per completed call, whichever is greater. Find the cost of a 1 minute call
s-1.75=0.02
Sketch the graph of function. f ( x ) =3x + 6 /x -1 Solution Thus, we'll start off with the intercepts. The y-intercept is, f (0) =6/-1=-6⇒ (0, -6)
7v+4(v+4)
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