Solving Logarithmic Equations

Solving Logarithmic Equations

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to solve a logarithmic equation involving natural logs and base conversion. It begins with an introduction to the problem and encourages viewers to engage by pausing and attempting the solution themselves. The tutorial then demonstrates the use of logarithmic properties and base conversion to simplify the equation. The instructor guides viewers through the process of solving for x, ultimately deriving the final expression. The video concludes with a summary of the solution and a call to action for viewers to like and subscribe.

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21 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial problem statement in the video?

Determine the roots of the quadratic equation x^2 - 4x + 4 = 0

Find the value of x in the equation ln(2x) + log(x) = 2

Solve for y in the equation y^2 + 3y = 2

Calculate the derivative of the function f(x) = x^2 + 3x

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the equation ln(2x) + log(x) = 2?

Simplify using the Power Rule

Convert all logarithms to the same base

Factor out common terms

Introduce the exponential function

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of the video tutorial?

To explain the change of base formula

To introduce exponential functions

To solve a logarithmic equation

To teach factoring techniques

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main focus of the video tutorial?

Introducing exponential functions

Solving a quadratic equation

Understanding logarithmic properties

Solving a logarithmic equation

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What property of logarithms is used to rewrite ln(2x)?

Change of Base Formula

Power Rule

Quotient Rule

Product Rule

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in simplifying the equation?

Convert to base 10 logarithm

Factor out common terms

Use properties of logarithms

Introduce the exponential function

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the logarithm in base 10 converted to a natural logarithm?

Using the Power Rule

Using the Product Rule

Using the Quotient Rule

Using the Change of Base Formula

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