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Chapter 3: Problem 27

Use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\ln \left(5 e^{6}\right)$$

Short Answer

Expert verified
\(\ln(5) + 6\)

Step by step solution

01

Identify known logarithmic identities

Note that we know from properties of logarithms that \(\ln(e^x) = x\). This identity can be applied because the base of the natural logarithm (ln) and the base of the exponential function are the same (both are e).
02

Apply the Identity

In the expression \(\ln(5e^6)\), we can apply the identity from Step 1 to the term \(e^6\). The logarithmic identity allows us to 'bring down' the exponent in \(e^6\), giving the simplified expression \(\ln(5) + 6\).
03

Final Simplification

Now the expression is simplified to \(\ln(5) + 6\). Since there's no further simplification possible, this is the final answer.

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Most popular questions from this chapter

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$6 \log _{3}(0.5 x)=11$$

A logistic curve is also called a ________ curve.

Use your school's library, the Internet, or some other reference source to write a paper describing John Napier's work with logarithms.

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln (x+5)=\ln (x-1)-\ln (x+1)$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x-\ln (x+1)=2$$
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