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.
= 2 + 4 = 6 … continued : … continued Example: Express as a single logarithm
log519 + log53 = log5(193)
= 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
X=2/5 THE END!!!! : THE END!!!!