Exponential Functions

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Exponentials : 

Exponentials By Dev & Deb

Inverse Relations & Functions : 

Inverse Relations & Functions Interchanging x and y in the equation of a relation produces an equation of the inverse relation Example: Write an equation of the inverse of y=x2-5. Because the inverse relation is the interchanging of x and y, you simply switch x to where y is, and vice versa. Your equation now should read: x=y2-5 Now, don’t forget to SOLVE for y! Y =

Exponential & Logarithmic Relationships : 

Exponential & Logarithmic Relationships Recall the following are equivalent: x=ay and logax Example: Convert to a logarithmic equation 2x=8 ---> x=log28 * The logarithm is the exponent

… Continued : 

… Continued It is also useful to be able to convert from a logarithmic equation to an exponential equation Example: Convert to an exponential equation Y=log35 ---> 3y=5

Properties of Logarithmic Functions : 

Properties of Logarithmic Functions loga(x  y)=loga x+loga y Example: Express as a sum of logarithms. Simplify if possible. Log2(416)=log24+log216 = 2 + 4 = 6

… continued : 

… continued Example: Express as a single logarithm log519 + log53 = log5(193) = log557

Exponential and Logarithmic Equations : 

Exponential and Logarithmic Equations Example: Solve log3(5x+7)=2 We already have a single logarithmic expression, so we write an equivalent exponential equation 5x+7=32 5x+7=9 X=2/5

THE END!!!! : 


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