Outcome: C24, solve exponential and logarithmic equations

Originator:  Daniel & Alex

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

2. Division law,

3. Power of a power,

4. Power of a product,

5. Power of a quotient,

6. Zero exponents,  

7. Negative exponents,  or

8. Rational exponents,

Also   &

To solve for y, plug in numbers.

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

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

To solve for d, 

To solve for c, simplify to  plug in then numbers (let  )   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 .

To Solve for x, simplify to  plug in then numbers (let  )   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: ) answers for (b to what power = x), and there are  three laws of logarthiums:

1. Log of a power, . 

2. Log of a product, . 

3. Log of a quotent, . 

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,  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.   

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

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

Example Question

Solve the following using logarithmic equations.

Question