# The exact value of e 2 ln 3 .

BuyFind

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 1, Problem 25RE

(a)

To determine

Expert Solution

## Answer to Problem 25RE

Solution:

The exact value of e2ln3=9.

### Explanation of Solution

Let y=e2ln3.

Then, the equation can be expressed as y=eln32.

Using the law, elnx=x,x>0, y=32

Thus, the exact value of e2ln3=9.

(b)

To determine

Expert Solution

## Answer to Problem 25RE

Solution:

The exact value of log1025+log104=2.

### Explanation of Solution

The given quantity is log1025+log104.

Use the law of logarithm, log10(xy)=log10x+log10y, express the given quantity as log1025+log104=log10(100).

Express 100 as a power of 10. That is log10100=log10102.

Use the law of logarithm, logb(bx)=x,x, simplify the quantity log10102 as 2.

Thus, the exact value of log1025+log104=2.

(c)

To determine

Expert Solution

## Answer to Problem 25RE

Solution:

The exact value of tan(arcsin12)=13.

### Explanation of Solution

Let y=tan(sin112).

The value of, sin112=π6

Thus, tan(sin112)=tan(π6) .

But the value of tan(π6)=13.

Thus, the exact value of tan(arcsin12)=13.

(d)

To determine

Expert Solution

## Answer to Problem 25RE

Solution:

The exact value of sin(cos145)=35.

### Explanation of Solution

Let x=cos1(45).

So, cosx=45.

Then, by Pythagoras theorem, sinx=35.

Thus, the exact value of sin(cos145)=35.

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