Your Algebra Homework Can Now Be Easier Than Ever!

Logarithms

Topic 5-4: Solving Logarithmic Equations

A logarithmic equation is an equation involving one
or more logarithmic expressions.

Logarithmic equations can be divided into two
families
:
1. Those equations that can be simplified into the form
of a logarithmic expression equal to a number .

2. Those equations that can be simplified into the form
of two logarithmic equations (same base) equal to
each other.

To solve the first case, apply the following steps :
1. Use the laws of logarithms , as necessary, to
combine logarithms .

2. Rewrite the logarithm equation into exponential
form.

3. Solve using any appropriate algebraic and/or
arithmetic
methods.

4. Check your solutions. Like radical equations ,
logarithmic equations can (and often do) produce
extraneous solutions.

Ex. 1 Solve.

Ex. 2 Solve.

Ex. 3 Solve.

Ex. 4 Solve.

If the equation is simplified (using the laws of
logarithms) in such a way both sides have a
logarithmic expression, consider the limited
possibilities for making the equation true...

Ex. 1 Solve.
 

Ex. 2 Solve.

log(x + 4) + log(x + 5) −log(1− x) = log(x + 7)

Topic 5-5: Solving Exponential Equations

An exponential equation is an equation involving
one or more exponential expressions.

Basic process to solve most exponential
equations:

1. Isolate an exponential expression on one side .

2. Take the natural logarithm (or common log) of both
sides.

3. Use the laws of logarithms to rewrite the exponential
expression so that no variable remains in the
exponent.

4. Apply basic algebraic and arithmetic manipulation to
solve for x.

5. Use the laws of logarithms to simplify the solution
and approximate the solution.

6. Check your solution.

With regards to step 5, I will expect you to further rewrite
the solution into a single logarithmic expression and
approximate five places after the decimal .

Ex. 1 Solve.

63x = 100

Ex. 2 Solve.

4 + 3x-2= 16

Ex. 3 Solve.

52x-1 = 18

Ex. 4 Solve.

102x+1 = 500

Ex. 5 Solve.

Exponential equations involving 2 exponential
expressions

If the bases are equal or the bases are both powers
of the same constant, solving the equation is fairly
easy.

Ex. 1 Solve.

Ex. 2 Solve.

If the bases are neither equal nor related, revert
back to the previously covered process for solving
exponential equations but more or less ignore step
1.

Ex. 1 Solve.

Ex. 2 Solve.

Ex. 3 Solve.

Exponential equations solved by substitution and
factoring

The important skill to remember here is
that

Ex. 1 Solve.

Ex. 2 Solve.

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of March 28th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2024, Algebra-Answer.Com.  All rights reserved.