2.5 Solving Logarithms

2.5 Solving Logarithms

by Christina Early

Multiple Choice

5 = 7s - 9

• 2
• 6
• 7
• 8

Multiple Choice

Solve for x:

2x -1(3+4x) = 11

• x = -4

• x = 7/3

• x = -7

• x = -17/8

Multiple Choice

Solve for k:

38 + 7k = 8(k + 4)

• k = 6

• k = 8

• k = -6

• k = 1

​Steps to solve Logarithmic Equations

1. ​Rewrite in Exponential Form (b^e=n)

2. ​Evaluate any exponents

   1. (plug into calculator)

3. ​Solve for variable

4. ​Check answer!

​Another Example

​One MORE example before you try on your own

Multiple Choice

$$\log_3v=4$$  

• 12

• 7

• 81

• 4

• 3

Multiple Choice

$$\log_5\left(a-5\right)=-2$$  

• 5.04

• 5

• -2

• 0.04

• -4.96

Multiple Choice

7log(9x-7)=0

*Hint: undo operations outside log FIRST!

• $$\frac{9}{8}$$  

• $$\frac{8}{9}$$  

• 0

• 1

• $$\frac{7}{9}$$  

​Solving Logarithms using equality Property

• ​IF log_bM=log_bN then M=N.

  • ​So same base get rid of based solve linear equation! just like exponentials

• ​Steps:

  • ​Cancel out logarithms AND BASES!!!!

  • ​Solve for the variable.

​Example #7

​Example # 8

​Example #9 on worksheet

Multiple Choice

$$\log_{18}27=\log_{18}r$$  

• 27

• 486

• 1.5

• 0.67

• 18

Multiple Choice

log 5n=log(4n+4)

• -5

• 5

• 4

• -4

• $$\frac{5}{4}$$  

Multiple Choice

$$\log_{12}\left(5v-8\right)=\log_{12}\left(4v+10\right)$$  

• 10

• 4

• 5

• 18

• 2

​Work on the back of your notes page

​Whatever you do not finish will be classwork tomorrow!

​

​I will post the answer key tomorrow on itslearning.