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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Solving Exponential and Logarithmic Equations In Exercises 67-80, solve for x.

ln x + ln ( x 4 ) = 0

To determine

To calculate: The value of x for the equation lnx+ln(x4)=0.

Explanation

Given Information:

The provided equation is lnx+ln(x4)=0.

Formula used:

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

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

The value of x for the equation ax2+bx+c=0 by using the quadratic formula is x=b±b24ac2x.

Calculation:

Consider the equation, lnx+ln(x4)=0

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

ln(x(x4))=0ln(x24x)=0

Take exponential of both sides as,

eln(x24x)=e0

Apply the inverse property of elnx as,

x24x=e0x24x=1

Subtract 1 on both sides as,

x<

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