# The equation, e 7 − 4 x = 6 for x .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.6, Problem 49E

(a)

To determine

## To Solve: The equation, e7−4x=6 for x.

Expert Solution

The value of x1.30225 .

### Explanation of Solution

The given equation is e74x=6 .

Taking natural log on both sides, ln(e74x)=ln6

Use the law of logarithm, ln(ex)=x,x express the above equation as 74x=ln6 .

To find the value of x, simplify further as follows.

7ln6=4x7ln64=xx71.7914x1.30225

Therefore, the value of x1.30225 .

(b)

To determine

### To solve: The equation, ln(3x−10)=2 for x.

Expert Solution

The value of x5.7964 .

### Explanation of Solution

The given equation is ln(3x10)=2 .

Raise to the power e on both sides, eln(3x10)=e2 .

Use the law of logarithm, elnx=x,x>0 and simplify further as follows.

3x10=e23x=e2+10x=e2+103x=7.389+103

Thus, the value of x5.7964 .

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