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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.

500 ( 1.075 ) 120 x = 100 , 000

To determine

To calculate: The value of x for the equation 500(1.075)120x=100,000.

Explanation

Given Information:

The provided equation is 500(1.075)120x=100,000.

Formula used:

The property of logarithms, lnxn=nlnx

Where x and y are real numbers greater than 0.

Calculation:

Consider the equation, 500(1.075)120x=100,000

Divide both sides by 500 as,

500(1.075)120x500=100,000500(1.075)120x=200

Take natural logarithm both sides as,

ln(1.075)120x=ln(200)

Apply the property of lnxn=nlnx as,

(120x)ln(1

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