## Properties of logarithms, Algebra

Assignment Help:

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 )

#### Convert following into the function, Convert following into the form    ...

Convert following into the form                                        f (x ) = a ( x - h ) 2  + k Solution We are going to complete the square here.  Though, it is a s

#### Quiz #5., Working together Jack and Bob can clean a place in 30 minutes. On...

Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?

-2

#### Solve the given log function, Example: Solve following equations. 2 log...

Example: Solve following equations. 2 log 9 (√x) - log 9 (6x -1) = 0 Solution  Along with this equation there are two logarithms only in the equation thus it's easy t

#### Solving for a variable, what are the steps to solving a variable like this ...

what are the steps to solving a variable like this one -3f=g for f

#### Percents, How do I figure out what is 20% of 100?

How do I figure out what is 20% of 100?

#### Pre algebra, i need help with linear functions in pre algebra i have a tes...

i need help with linear functions in pre algebra i have a test tomorrow and i need help with the concept and ways to remeber it thank you! mackenzie

y=(3x+3)

#### Expressions and inequlites, A blue whale gains 2.3 tons a month for the fir...

A blue whale gains 2.3 tons a month for the first year of life. If a blue whale weighed 15 tons at birth, how much will it weigh on its first birthday?

#### Logarithms, Log(8)10 Find the approximation and exact value. log(5)317 Fi...

Log(8)10 Find the approximation and exact value. log(5)317 Find the approximation and exact value  