Solving Exponential Equations with Logarithms

This video tutorial teaches how to solve equations where the variable is in the exponent and the base is 2, using logarithms. It covers the use of both common and natural logs, addresses common misunderstandings, and provides examples using tables for approximation. The tutorial also includes an advanced example of isolating the base before applying logarithms.

What is the main focus of this lesson regarding solving equations?

• Solving equations with variables in the constant

• Solving equations with variables in the coefficient

• Solving equations with variables in the exponent

• Solving equations with variables in the base

When using tables to solve 2^x = 20, what is the approximate value of x?

• 4.7

• 4.5

• 4.3

• 4.1

What is a common misunderstanding when working with logarithms?

• Logarithms are always positive

• Logarithms cancel each other out

• Logarithms can be multiplied directly

• Logarithms can be added directly

What property allows the exponent to be moved in front of the logarithm?

• Logarithm of a sum

• Logarithm of a quotient

• Logarithm of a product

• Logarithm of a power

How can you solve for x using common logs in the equation 2^x = 20?

• Add the log of 2 to the log of 20

• Divide the log of 20 by the log of 2

• Multiply the log of 20 by the log of 2

• Subtract the log of 2 from the log of 20

What must be done before using logarithms to solve an equation with a variable in the exponent?

• Isolate the base

• Add the base to both sides

• Subtract the base from both sides

• Multiply both sides by the base

What is the exact answer for x in the equation 5x * ln(2) = ln(14)?

• 5ln(2) / ln(14)

• ln(2) / ln(14)

• ln(14) / 5ln(2)

• ln(14) / ln(2)