Solving Equations with Exponents Using Common Logarithms

This video tutorial teaches how to solve equations where the variable is in the exponent using common logarithms. It covers the properties of logarithms, including the key property that log base 10 of 10 to the X equals X. The tutorial demonstrates solving equations using graphs and calculators, addresses common misunderstandings, and explores advanced applications of logarithms. The focus is on base 10 logarithms, known as common logarithms, and their use in simplifying and solving exponential equations.

What is the main focus of this lesson?

• Solving linear equations

• Solving equations with variables in the exponent using common logarithms

• Understanding the history of logarithms

• Learning about different types of logarithms

What is the result of log(100) using a calculator?

• 1

• 2

• 3

• 4

What does the property log(10^X) = X imply?

• The logarithm of any number is zero

• The exponent on 10 is equal to the logarithm

• The base of the logarithm is always 2

• The logarithm of 10 is always 10

Why might using a graph to solve exponential equations be challenging?

• Exponential functions are not real numbers

• Exponential functions involve very large or small numbers

• Graphs are not accurate

• Graphs are only for linear equations

What is a common mistake when using logarithms with different bases?

• Using a calculator for logarithms

• Assuming log(10^X) = X applies to all bases

• Using the wrong logarithm button

• Forgetting to multiply by the base

How do you solve for X in the equation 10^(5X) = 5000?

• Multiply both sides by 5

• Take the common log of both sides and divide by 5

• Subtract 5 from both sides

• Add 5 to both sides

What should you do before applying logarithm properties in an equation?

• Get the base by itself

• Add a constant to both sides

• Subtract the exponent from both sides

• Multiply both sides by the base