	Algebra Tutorials!

	Thursday 21st of November



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	Scientific Notation
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	Linear Equations and Inequalities in One Variable
	Graphing Equations in Three Variables
	What the Standard Form of a Quadratic can tell you about the graph
	Simplifying Radical Expressions Containing One Term
	Adding and Subtracting Fractions
	Multiplying Radical Expressions
	Adding and Subtracting Fractions
	Multiplying and Dividing With Square Roots
	Graphing Linear Inequalities
	Absolute Value Function
	Real Numbers and the Real Line
	Monomial Factors
	Raising an Exponential Expression to a Power
	Rational Exponents
	Multiplying Two Fractions Whose Numerators Are Both 1
	Multiplying Rational Expressions
	Building Up the Denominator
	Adding and Subtracting Decimals
	Solving Quadratic Equations
	Scientific Notation
	Like Radical Terms
	Graphing Parabolas
	Subtracting Reverses
	Solving Linear Equations
	Dividing Rational Expressions
	Complex Numbers
	Solving Linear Inequalities
	Working with Fractions
	Graphing Linear Equations
	Simplifying Expressions That Contain Negative Exponents
	Rationalizing the Denominator
	Decimals
	Estimating Sums and Differences of Mixed Numbers
	Algebraic Fractions
	Simplifying Rational Expressions
	Linear Equations
	Dividing Complex Numbers
	Simplifying Square Roots That Contain Variables
	Simplifying Radicals Involving Variables
	Compound Inequalities
	Factoring Special Quadratic Polynomials
	Simplifying Complex Fractions
	Rules for Exponents
	Finding Logarithms
	Multiplying Polynomials
	Using Coordinates to Find Slope
	Variables and Expressions
	Dividing Radicals
	Using Proportions and Cross
	Solving Equations with Radicals and Exponents
	Natural Logs
	The Addition Method
	Equations

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Finding Logarithms

You can find the value of some logarithms by first writing them in exponential form. Once the equation is in exponential form, you can solve it using the Principle of Exponential Equality.

Note:

Recall that the Principle of Exponential Equality states that if b^x = b^y, then x = y.

Here, b > 0 and b ≠ 1.

Example 1

Find log₂32.

Solution

Let x equal log₂32 to create an equation.

Rewrite in exponential form.

Rewrite 32 as 2⁵.

Use the Principle of Exponential Equality.

log₂32 = x

2^x = 32

2^x = 2⁵

x = 5

So, log₂32 = 5.

Here is a check:

Is log₂32 = 5 ?

Is 2⁵ = 32 ?

Is 32 = 32 ? Yes

Example 2

Find log₅1.

Solution

Let x equal log₅1 to create an equation.

Rewrite in exponential form.

Rewrite 1 as 5⁰.

Use the Principle of Exponential Equality.

log₅1 = x

5^x = 1

5^x = 5⁰

x = 0

Thus, log₅1 = 0.

Note:

Sometimes one side of an exponential equation cannot be easily rewritten as a power with the same base as the other side. Later, you will learn how to solve such equations.

Example 3

Find