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Chapter 3: Problem 43

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(1 .\) Where possible, evaluate logarithmic expressions without using a calculator. $$\ln x+\ln 7$$

Short Answer

Expert verified
The expression \(\ln x + \ln 7\) simplifies to \(\ln (7x)\).

Step by step solution

01

Identify the Logarithmic Property to Use

The logarithmic property that can be used here is the property stating that the sum of two logs with the same base can be written as the log of the product of their arguments. So, \(\ln a + \ln b\) can be written as \(\ln (ab)\).
02

Apply the Logarithmic Property

Applying this property to the given expression \(\ln x + \ln 7\), it can be written as a single logarithm, \(\ln (x*7)\).
03

Simplify the Expression

The expression \(\ln (x*7)\) simplifies to \(\ln (7x)\). This is the single logarithm whose coefficient is 1, as requested in the problem.

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