Question

Solve equation. $\log _{3}(4 c+5)=3$

Name: Problem 40, Chapter 13: Beginning and Intermediate Algebra
Uploaded: 2020-06-25T19:45:30-08:00
Duration: 28 s
Channel: Amy Jiang
Description: Solve equation. log3(4 c+5)=3

   Solve equation.
$\log _{3}(4 c+5)=3$

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 13, Problem 40

Instant Answer

Solved by Expert Amy Jiang

06/25/2020

Step 1

This gives us: $$3^3 = 4c + 5$$ Show more…

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Solve equation. $\log _{3}(4 c+5)=3$

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Key Concepts

Definition of Logarithms

A logarithm is the inverse operation to exponentiation. It indicates the power to which a given base must be raised to produce a certain number. For example, in the expression log_a(b) = c, the base a raised to the power c equals b.

Conversion Between Logarithmic and Exponential Form

One of the key steps in solving logarithmic equations is rewriting them in their equivalent exponential form. This is based on the principle that if log_a(b) = c, then b = a^c, which simplifies finding the value of the unknown variable.

Solving Linear Equations

After converting a logarithmic equation to its exponential form, the resulting equation is often a linear equation. Solving this linear equation involves isolating the variable using standard algebraic techniques such as addition, subtraction, multiplication, and division.

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