Exponential and Logarithm Conversion

Logarithmic functions are the inverse of...

• Linear Functions

• Exponential Functions 

• Quadratic Functions 

• Polynomial Functions 

How are exponentials and logarithms related?

• They're cousins

• They're inverses

• They're not related

• They're reciprocals

What is the base?

• 1

• 5

• 10

• 3

Rewrite in exponential form.

• A

• B

• C

• D

Given log₂₀ 0.05 = x, Complete the steps to evaluate by using exponential form. ​Step 1 (Rewrite in exponential form): ​ (a)   = 0.05 Step 2 (rewrite the decimal as a fraction): 0.05 = ​ (b)   Step 3 (reduce the fraction): ​ (c)   Step 4 (rewrite as an exponent): ​ (d)   Answer: ​ (e)  

Given log₂₀ 0.05 = x, Complete the steps to evaluate by using exponential form. Step 1 (Rewrite in exponential form): ​ (a)   = 0.05 Step 2 (rewrite the decimal as a fraction): 0.05 = ​ (b)   Step 3 (reduce the fraction): ​ (c)   Step 4 (rewrite as an exponent): ​ (d)   Answer: ​ (e)  

Given log₂₀ 0.05 = x, Complete the steps to evaluate by using exponential form. ​Step 1 (Rewrite in exponential form): ​ (a)   = 0.05 Step 2 (rewrite the decimal as a fraction): 0.05 = ​ (b)   Step 3 (reduce the fraction): ​ (c)   Step 4 (rewrite as an exponent): ​ (d)   Answer: ​ (e)  

Match each exponential expression to its equivalent logarithmic form.

• x¹⁰ = 3

• log₃ 10 = x

• e^x ≈ 10

• log_x 3 = 10

• e¹⁰ ≈ x

• log x = 3

• 10³ = x

• ln x ≈ 10

• 3^x = 10

• ln 10 ≈ x

Given log₂₀ 0.05 = x, Complete the steps to evaluate by using exponential form. Step 1 (Rewrite in exponential form): ​ (a)   = 0.05 Step 2 (rewrite the decimal as a fraction): 0.05 = ​ (b)   Step 3 (reduce the fraction): ​ (c)   Step 4 (rewrite as an exponent): ​ (d)   Answer: ​ (e)  

Rewrite the equation into logarithmic form:
6² = 36

• log₆ 2 = 36

• log₆ 36 = 2

• ln 36 = 2

• 6³⁶ = 2