Solving Logs and Exponentials

Solving Logarithm Equations

By Dr KEE CH

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Attach an exponent to the base number to make the equation true.

Learning objectives:

1. ​Student will be able to choose the correct law of logarithm to solve equations.

2. Student will be able to relate the key links between logarithms and exponentials.

3. Student will be able to apply solving exponential and logarithm equations to real world situations.​

Quick recap

Change of base

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Rewrite $$\log_25$$  to base 10

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Rewrite $$\log_25$$  to base 9

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Use the change of base formula to evaluate each expression. Round to four decimal places. Show your work. $$\log_261$$  

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Use the change of base formula to evaluate each expression. Round to four decimal places. Show your work. $$\log_{11}136$$  

Solve equation algebraically.

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$$12\log\left(3x-1\right)=36$$  

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$$4\log_5\left(x-1\right)-3=9$$  

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$$\log_{18}\left(10-2b\right)=\log_{18}\left(5b-4\right)$$  

Collaboration time!

​Click on the link and go to Jamboard

Check your understanding!

Multiple Choice

$$\ln\left(4\right)\approx$$  

• 1.386

• 1.863

• 1

• 4

Multiple Choice

Without using your calculator... $$\log\left(100\right)=$$  

• 1
  

• 2

• 1.5

• 3

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

$$\log_{18}27=\log_{18}r$$  

• 27

• 486

• 1.5

• 0.67

• 18

Multiple Choice

Convert this equation 19⁸ = x, to Logarithmic Form. 

• Log₈x = 19

• Log_x19 = 8

• Log₈x = 19

• Log₁₉x = 8

The base of the log is 10 and the base of the the exponent is also 10.

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What is your key takeaway from today's lesson?