Solved examples: Converting logarithmic to exponential form step-by-step.

📚 Quick Study Guide

• 🔑 The logarithm form is expressed as: $log_b(x) = y$
• 🔄 The exponential form is expressed as: $b^y = x$
• 📝 $b$ represents the base in both forms.
• 📍 $x$ is the argument of the logarithm and the result of the exponentiation.
• 📈 $y$ is the exponent and the value of the logarithm.
• 💡 To convert from logarithmic to exponential form, identify $b$, $x$, and $y$ in the logarithmic equation and rearrange them into the exponential equation.
• ➕ Remember that the base of the logarithm becomes the base of the exponential expression, the logarithm's result becomes the exponent, and the logarithm's argument becomes the result of the exponential expression.

🧪 Practice Quiz

1. What is the exponential form of $log_2(8) = 3$?
   1. 2⁸ = 3
   2. 2³ = 8
   3. 8² = 3
   4. 3² = 8
2. Convert $log_{10}(100) = 2$ to exponential form.
   1. 10¹⁰⁰ = 2
   2. 10² = 100
   3. 2¹⁰ = 100
   4. 100² = 10
3. Rewrite $log_5(25) = 2$ in exponential form.
   1. 5²⁵ = 2
   2. 2⁵ = 25
   3. 5² = 25
   4. 25² = 5
4. What is the exponential equivalent of $log_3(9) = 2$?
   1. 3⁹ = 2
   2. 3² = 9
   3. 9³ = 2
   4. 2³ = 9
5. Convert $log_4(16) = 2$ into exponential form.
   1. 4¹⁶ = 2
   2. 4² = 16
   3. 16⁴ = 2
   4. 2⁴ = 16
6. Rewrite $log_7(49) = 2$ in exponential form.
   1. 7⁴⁹ = 2
   2. 7² = 49
   3. 49⁷ = 2
   4. 2⁷ = 49
7. What is the exponential form of $log_6(36) = 2$?
   1. 6³⁶ = 2
   2. 6² = 36
   3. 36⁶ = 2
   4. 2⁶ = 36