Converting Exponential and Logarithmic

Rewrite 3⁴ = 81 in logarithmic form.

• log₃ 4 = 81

• log₈₁ 3 = 4

• log₃ 81 = 4

• log₄ 81 = 3

Change to Exponential Form:

log₆ 36 = 2

• 2⁶=36

• 6²=36

• 36²=6

• 36⁶=2

Rewrite the equation into logarithmic form:

6² = 36

• log₆ 2 = 36

• log₆ 36 = 2

• ln 36 = 2

• 6³⁶ = 2

Match each exponential expression to its equivalent logarithmic form.

• x¹⁰ = 3

• ln 10 ≈ x

• 10³ = x

• log₃ 10 = x

• 3^x = 10

• ln x ≈ 10

• e¹⁰ ≈ x

• log_x 3 = 10

• e^x ≈ 10

• log x = 3

Mathematical Equivalence

ON

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)  

Mathematical Equivalence

ON

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)