   Chapter 4.4, Problem 61E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Solving Exponential and Logarithmic Equations In Exercises 47–68, solve for x or t. See Examples 5 and 6. ln x − ln ( x − 6 ) = 3

To determine

To calculate: The value of x for the equation lnxln(x6)=3.

Explanation

Given Information:

The provided equation is lnxln(x6)=3.

Formula used:

The property of logarithms for the expression ln(xy) is ln(xy)=lnxlny where x and y are real numbers greater than 0.

The inverse property of exponents for the expression elnx is elnx=x.

Calculation:

Consider the equation, lnxln(x6)=3

Apply the property of ln(xy) in the above equation as,

ln(xx6)=3

Take exponential of both sides as,

eln(xx6)=e3

Apply the inverse property of elnx as,

xx6=e3

Now, multiply both sides by (x6) as,

xx6x

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