Converting Between Logs and Exponentials

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Rewrite each logarithmic equation as an exponential equation and vise versa

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)  

Match each logarithmic expression to its equivalent exponential form.

• x¹⁰ = 5

• log₅ 10 = x

• 10⁵ = x

• ln x ≈ 10

• e¹⁰ ≈ x

• ln 10 ≈ x

• 5^x = 10

• log x = 5

• e^x ≈ 10

• log_x 5 = 10

Match the following

Mathematical Equivalence

ON

Write 5^x =10 in log form

• x = log 5

• x = log₅10

• x = 5 log10

• x = 10 log 5