Question

Solve each equation. Check your answers. $$ 2 \log (x+1)=5 $$

   Solve each equation. Check your answers.
$$
2 \log (x+1)=5
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 8, Problem 40

Instant Answer

Solved by Expert Amrita Bhasin

08/10/2019

Step 1

Step 1: First, we can isolate the logarithm by dividing both sides of the equation by 2: $$ \log (x+1)=\frac{5}{2} $$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve each equation. Check your answers. $$ 2 \log (x+1)=5 $$

Play audio

Feedback

Powered by NumerAI

Amrita Bhasin and 63 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Properties of Logarithms

This concept involves understanding that logarithms are the inverse operations of exponentiation. For instance, in the equation log_b(y) = c, the relationship can be expressed in exponential form as b^c = y. Recognizing this property is crucial for rewriting and solving logarithmic equations.

Exponential Form Conversion

Converting a logarithmic equation into its equivalent exponential form is a key strategy in solving such equations. By rewriting an equation like log_b(y) = c as y = b^c, one can easily isolate the variable and solve the equation.

Solution Verification

After finding a solution to a logarithmic equation, it is important to substitute the solution back into the original equation. This step ensures that the solution not only satisfies the equation mathematically but also adheres to the necessary domain restrictions of logarithms.

Domain of Logarithmic Functions

The argument of a logarithmic function must be positive, as logarithms are only defined for positive real numbers. This domain restriction is essential when solving logarithmic equations because any potential solution must ensure that the input to the logarithm remains greater than zero.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later