Question

Solve each equation. $$ \ln 4+\ln x=5 $$

Name: Problem 65, Chapter 9: Algebra 2
Uploaded: 2020-02-08T18:29:29-08:00
Duration: 1 min 18 s
Channel: Charles Carter
Description: Solve each equation. ln4+lnx=5

   Solve each equation.
$$
\ln 4+\ln x=5
$$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 9, Problem 65

Instant Answer

Solved by Expert Charles Carter

02/08/2020

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Step 1: We start with the given equation: $$ \ln 4+\ln x=5 $$ Show more…

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Solve each equation. $$ \ln 4+\ln x=5 $$

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Key Concepts

Exponential and Logarithmic Equations

Solving logarithmic equations often involves rewriting the equation in exponential form. When an equation of the form ln(y) = k appears, it can be converted to y = e^k, which is crucial for isolating and finding the value of the variable.

Algebraic Manipulation

Once logarithmic properties are applied and the equation is in exponential form, further algebraic manipulation is used to isolate the variable. This step involves basic operations such as multiplication or division to solve for the unknown.

Properties of Logarithms

The logarithm addition property, ln(a) + ln(b) = ln(ab), allows the combination of two logarithmic expressions into one. This property simplifies the process of solving logarithmic equations by consolidating multiple logs into a single term.

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