M2.+Use+logarithms+to+solve+exponential+equations.

This is the standard of M2. which is solving exponential equations using logarithms.


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**1. What you need to understand.**
Logarithms are used in solving exponential problems and in order to answer the problems, the following rules must be applied.
 * log(a)=b
 * 10^b=a


 * calculators are powerful tools in this standard and have a log button *

Example 1: If [[image:Screen_shot_2011-05-31_at_9.32.23_AM.png width="24" height="17"]]=8545, what does x=? (Round to nearest tenth)
We know--> = a

Put this knowledge into a log equation--> log(a)= 8545

Answer--> log(8545)= 3.9 x= 3.9

Example 2: If [[image:Screen_shot_2011-05-31_at_9.57.19_AM.png width="34" height="19"]] = 100,000, what does x=?
We know--> = a

Put this knowledge into a log equation--> log(100,000) = 5

This would be the answer, but because it is x+2 you will subtract 2 from 5 to take into acount what was added--> 5-2 = 3 x = 3

Example 3: (Harder problem) 7log(2x) = 14 Find x
Divide both sides by 7--> We know that 14/7 (2) is the exponent and we can also plug in the base 10--> Divide both sides by 2 to get x alone--> Answer--> x = 5

Example: Log x= 10 What is x?
Mistake: Many students substitute the 10 for x which would solve for 1. Correction: Because we know ﻿=a, that means the number is in base ten.

New Equation: which equals 10,000,000,000.

Answer: x = 10,000,000,00

Helpful websites:
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Helpful pages in your textbook:
Page 379 Page 384 question 5.