Algebra Tutorials!
Saturday 15th of June  
Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Angles and Degree Measure
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Solving Exponential Equations

Example 1



Each side of the equation contains an expression with base e. However, in the expression on the right, the base e is in the denominator.

Therefore, we use the definition of a negative exponent to write the expression on the right with in the numerator.

Original equation. e2x - 6
Rewrite the right side.

Remove the parentheses.

Use the Exponential Equality Property.

Add x to both sides.

Add 6 to both sides.

Divide both sides by 3.

e2x - 6

e2x - 6

2x - 6

3x - 6



= e -(x - 9)

= e - x + 9

= -x + 9

= 9

= 15

= 5

So, the solution of is x = 5.


Recall the definition of a negative exponent:


Example 2

The point (2, 25) lies on the graph of the exponential function y = bx.

Find the base, b, of this exponential function.


Since (2, 25) lies on the graph, we know that x = 2 when y = 25 in the exponential function. y = bx
Replace y with 25 and x with 2.

Write 25 as 52.

Since the exponents are the same, the bases are equal.

So, the base, b, of the exponential function is 5.

We can now write the exponential function:

As a check, find f(2).







= b2

= b2

= b


= 5x

= 52

= 25

This results in the original ordered pair, (2, 25), as expected.


Note that if 52 = b2 then b could also be -5.

However, we are working with an exponential function.

That means the base, b, must be such that b > 0 and b 1.

Thus, b must be positive 5.

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