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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 )
Solve the following simultaneous equations by using Cramer's rule 3x+2y=13 2x-y=4
A team needs to save up $400 for new uniforms and currently has $190. They decide to hold a fundraiser where they can earn a $7 profit for each item sold. What equation could be s
x
We should graph a couple of these to make sure that we can graph them as well. Example : Sketch the graph of the following piecewise function. Solution Now while w
I am a first time algebra student and am confused. Can you give me step by step equations on how to calculate 5+2x=2x+6
3x + 5 = 12
add - 3a + b - 10 -6c, c -d- a + 9 and - 4c +2a - 3b - 7
ue Week 7 and worth 55 points Five (5) years ago, you bought a house for $171,000, with a down payment of $30,000, which meant you took out a loan for $141,000. Your interest rate
a^2-b^2-c^2-2bc
(4y2)(2y)
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