Everything about Exponential and Logarithmic Functions.

Students complain that exponential and logarithmic equations are hard for them. The reason is not that they are hard, but that they have been taught most of the time; assuming that students don't need a detailed solution, but a solution that skips "irrelevant" steps.

This lesson covers the topic with examples that don't assume that the student doesn't need the intermediate steps. You will really like it!

Lesson's Content


Lesson In PDF Format (no animations)

Lesson's Glossary

Exponent: It is a raised number representing the repeated multiplication of a given factor.

Exponential equation: Equation with variables in the exponent (s)

Exponential function: Any equation of the form y = bx that has a variable as exponent. Exponential functions and logarithmic functions are inverses each other.

Logarithm (log): log_b x is the power to which the base b needs to be raised in order to get x.

Logarithmic equation: An equation that contains logarithmic expressions.

Logarithmic function: Any function of the form y = log_b x

Logarithmic functions and Exponential functions are inverses.

Natural logarithm: y = ln x is the natural log or logarithm to the base e or y = log_b x.

Natural logarithmic function: A function with a natural logarithm expression.

Power: Exponent of a number or variable.

Principal root: Given a number with two roots, the positive root is the principal and its given by the radical sign.

Rational exponent: Given that the nth root of x is a real number and m is an integer, we have that x1/n = n√x and xm/n = n√xm= (n√a)n.

Rational number: Any number that may written as a fraction; including whole numbers (written as fractions with 1 as denominator) and decimals that truncate or repeat (may be expressed as fractions).

Term: A form of grouping one or more numerical and/or variable factors by means of multiplication and division. Addition and subtraction symbols separate terms.

Variable: A letter used to represent a number. When the variable is part of an equation, it is possible to find the value for which it stands for by solving the equation. This is the solution (s) of the equation.

Variable expression: Mathematical phrase with at least one variable in it.

Radical: The symbol that encloses a square root or any other given root.

Radicand: The number that is under the radicand sign.

Interactive Algebraic Applets

Logarithmic and exponential functions are inverses.

Drag the slider for "b" to view updated versions of

logarithmic and exponential functions in the

algebraic applet. You may drag point in the logarithmic

graph to view values for a specific graph set.

This interactive algebraic applet presents in a dynamic

way a proof for the product, quotient, and power properties

for logarithms. If you want to verify its accuracy, set the

value for "b" at 10, and use the common logarithm of your

calculator.

Calculators only have common logarithms, or logarithms with base 10,

and natural logarithms, or logarithms with base "e". This applet allows you

to verify the change of base formula. You may also check how logarithms

with the same base in an equality have the same number.

Play with the algebraic interactive applet to have some fun!

Vocabulary Puzzle

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