Show:
Graphing Exponential Functions
Graphing Logarithmic Functions
Solving Exponential Equations
Solving Logarithmic Equations
Properties of Logarithms:
PR Property
Q Property
PO Property
100
a geometric figure divided into pieces which are similar in shape, but smaller than the original figure.
What is A fractal
100
f(x) = log(4)x or f(x) = log x over log 4
What is the Change of Base formula
100
represents the reciprocal of its base.
What is a negative exponent
100
states that given an equation where two logarithmic expressions, with identical bases, are equal to each other, the arguments of those expressions are also equal.
What is the equality property
100
When multiplying two of the same variable, add the exponents. Fractions must have common denominators before being added.
What is product property
200
a function where the variable is located in the exponent and the base of the function is a positive real number not equal to 1.
What is An exponential function
200
it is simply a reflection of its exponential function counterpart across the line y = x.
What is the graph of a logarithmic function
200
one in which a variable occurs in the exponent.
What is an exponential equation
200
they contain logarithmic expressions and constants.
What are logarithmic equations
200
When a power is raised to another power, multiply the exponents. To multiply fractions, multiply the numerators, multiply the denominators, and then simplify the product.
What is power if a power property
300
Imaginary lines that a function or an equation approaches more and more closely
What is an asymptote.
300
the inverse of an exponential function
What is a logarithmic function
300
1. Isolate the exponential expression. 2. Take log or ln of both sides. 3. Solve for the variable.
What is how to solve most exponential equations
300
Write as one log isolated on one side.Use the definition of logarithms to write in exponential form.Solve for x.
What are steps to solve logarithmic equations
300
When dividing two of the same variable, subtract the exponents. Fractions must have common denominators before being subtracted.
What is quotient property
400
f(x) = a^x where a > 0 and a doesn't = 0
What is the form of the definition of an exponential function.
400
they have a domain of x > 0, a range of all real numbers and a vertical asymptote at x = 0.
What is general logarithmic functions
400
solve 4^x+1 = 4^9
What is x=8
400
Solve log2(x) = 4.
What is x = 3
400
any number that can be written as a fraction, so long as the denominator does not equal 0.
What is a rational number
500
it changes the base into a fraction!
What is a negative exponent
500
Open GeoGebra. In the “View” menu make sure that “Axes,” “Grid,” “Algebra View,” and “Input Bar” are all checked. Enter the equation f(x) = lg(x)/lg(4) in the “Input” field. The term “lg” is used to indicate a logarithm. Be sure there is no space between “lg” and the argument of x and base of 4. The argument of each logarithm must be surrounded by parentheses. After entering the function, the graph will appear.
What are steps to graph logarithmic functions using geogebra
500
Solve 4^x = 7^x+1
What is x= -3.48
500
Solve log2(x) + log2(x – 2) = 3
What is x = 4
500
to solve them, you need to isolate the constant terms on one side of the equation. Isolate the logarithmic terms on the other side. Then, convert the logarithmic equation into an exponential equation.
What are Logarithmic Equations with Constants