Solving Logarithmic Equations
-
Upload
kasimir-steele -
Category
Documents
-
view
27 -
download
0
description
Transcript of Solving Logarithmic Equations
Solving Logarithmic Equations
We need to solve log equations to find the
y intercept. We’ll use the log properties to help us do that.
5𝑥−3=32𝑥−1Type 1:
5𝑥−3=32𝑥−1Take the Log or In of both sides.
𝑙𝑜𝑔5𝑥− 3=𝑙𝑜𝑔32𝑥−1Use the power property to bring the
exponents down.(𝑥−3)𝑙𝑜𝑔5❑=(2𝑥−1) 𝑙𝑜𝑔3❑
Use the power property to bring the exponents down.
(𝑥−3)𝑙𝑜𝑔5❑=(2𝑥−1) 𝑙𝑜𝑔3❑
Remember log5 and log3 are just decimals so we can either distribute them through and
then collect like terms, etc. OR….
(𝑥−3)𝑙𝑜𝑔5❑=(2𝑥−1) 𝑙𝑜𝑔3❑Or divide both sides by one of them
𝑙𝑜𝑔5❑𝑙𝑜𝑔5❑
(𝑥−3)❑=(2 𝑥−1 )( .𝟔𝟖𝟐𝟔)Distribute, collect like-terms, etc.
x – 3 = 1.36x - .6826-1.36x + 3 -1.36x +3
x – 3 = 1.36x - .6826x =-6.437
Your turn…..
3𝑥−3=92 𝑥+1
Your turn…..
𝑒𝑥−3=5
Type 2:𝑙𝑜𝑔6 (5 𝑥−3 )=𝑙𝑜𝑔66 𝑥Notice:1. log with same base on both sides.2. logs are ALONE. Nothing is multiplied or added on.For example:𝟐 𝒍𝒐𝒈𝟔 (𝟓 𝒙−𝟑 )=𝒍𝒐𝒈𝟔𝟔 𝒙𝟐 𝒍𝒐𝒈𝟔 (𝟓 𝒙−𝟑 )=𝒍𝒐𝒈𝟔𝟔 𝒙+𝟏𝟎
Type 2:𝑙𝑜𝑔6 (5 𝑥−3 )=𝑙𝑜𝑔66 𝑥
When we have THIS situation and
this situation ONLY the logs can be cancelled.
Type 2:𝑙𝑜𝑔6 (5 𝑥−3 )=𝑙𝑜𝑔66 𝑥
5x - 3And then
it’s easy to solve!
Type 3:𝑙𝑜𝑔6 (5 𝑥−3 )=12
Notice: ONLY one “log”So MUST rewrite into
exponential form
Type 3:𝑙𝑜𝑔6 (5 𝑥−3 )=12
𝟔𝟏𝟐=𝟓 𝒙−𝟑And then
it’s easy to solve!
p. 519 4- 36 evens