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C24

Page history last edited by PBworks 13 years, 7 months ago

Outcome: C24, solve exponential and logarithmic equations

 

Originator:  Daniel & Alex

 

Explanation: To solve exponential equations  you must simplify the problem until you get to Formula where 

a=y intercept, b=common ratio, c= incramint of time needed to change by b, d=horizonal asymptote. 

There are eight laws of expontents:

 

1. Multiplacation law, Formula

 

2. Division law, Formula

 

3. Power of a power, Formula

 

4. Power of a product, Formula

 

5. Power of a quotient, Formula

 

6. Zero exponents, Formula Formula

 

7. Negative exponents, Formula or Formula

 

8. Rational exponents, Formula

 

Also  Formula & Formula

 

To solve for y, plug in numbers.

 

To solve for a, set Formula and plug in the other numbers.

 

To solve for b, Formula f1 is first value given f2 is the second.

 

To solve for d, Formula

 

To solve for c, simplify to Formula plug in then numbers (let Formula )  Formula then find when U is base b to the power of something then set the two powers equil (if this number is irrational see logarthums below), and then multiply both sides by c then devide by the power that you found (swiching c and the power) so it becomes Formula.

 

To Solve for x, simplify to Formula plug in then numbers (let Formula )  Formula then find when U is base b to the power of something then set the two powers equil (if this number is irrational see logarthums below), and then multiply by c.  

 

Logarthiums are a nother way to solve for the value of x in a exponatial equation. Logs are used to solve for irrational ( numbers that can't be expressed as a fraction ex: Formula) answers for (b to what power = x), and there are  three laws of logarthiums:

 

1. Log of a power, Formula

 

2. Log of a product, Formula

 

3. Log of a quotent, Formula

 

Logs are the inverse of exponents, much the same way  as addition is the inverse of subtraction, division is the inverse of multiplecation, or roots are the inverse of powers.

 

To solve with logarthums we must re-wite the equation, Formula This makes the exponential equation a logarithmic one. 

 

 The base stays the same but x and y (the argument and the solution) values swich. Once it is in a logarithmic equation and the base is not 10 you must make it 10, so you can solve it in a calculator (ex: Ti-83).  

To make the logarithium base 10 u must use the change of base formula. Formula  

this gives you the irrational (but works with rational also) number then when you have the base to the power of this number equils the base to the power of x/c. 

Then to find x multiply the by c. To find c multiply both sides by c then devide by the power that you found (swiching c and the power) so it becomes Formula

 

 

Note: If the base of the log is not given it is (base)10 so Formula

 

 

 

Example Question

 

Solve the following using logarithmic equations.

 

 

Question 

Formula 

 

 

Formula 

 

 

Formula

 

 

Formula

 

 

Formula

 

 

Formula 

 

 

Formula

 

 

Formula

 

 

Formula

 

 

Formula

 

 

 

Comments (1)

Anonymous said

at 9:47 pm on Apr 29, 2007

Looks great guys. You've picked up LaTex really fast. It makes the page look really professional. You still have a number of spelling errors however.

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