http://www.ck12.org Chapter 3. Logs and Exponents
log 1. 798982 x=log 1. 798986
2 x·log 1. 79898 = 6 ·log 1. 79898
2 x= 6
x= 3Vocabulary
Taking the log of both sidesis an expression that refers to the action of writing log in front of the entire right hand
side of an equation and the entire left hand side of the equation. As long as neither side is negative or equal to zero
it maintains the equality of the two sides of the equation.
Guided Practice
- Solve the following equation for all possible values ofx:(x+ 1 )x−^4 − 1 = 0
- Light intensity as it travels at specific depths of water in a swimming pool can be described by the relationship
betweenifor intensity anddfor depth in feet. What is the intensity of light at 10 feet?
log( 12 i)=− 0. 0145 ·d - Solve the following equation for all possible values ofx.
ex−e−x
3 =^14Answers:
1.(x+ 1 )x−^4 − 1 = 0
(x+ 1 )x−^4 = 1
Case 1 is thatx+1 is positive in which case you can take the log of both sides.
(x− 4 )·log(x+ 1 ) = 0
x= 4 , 0Note that log 1= 0
Case 2 is that(x+ 1 )is negative 1 and raised to an even power. This happens whenx=−2.
The reason why this exercise is included is because you should not fall into the habit of assuming that you can take
the log of both sides of an equation. It is only valid when the argument is strictly positive.
- Givend=10, solve forimeasured in lumens.