The video tutorial explains how to simplify expressions involving natural logarithms and exponential equations. It covers the use of properties to simplify expressions like natural log of e to the 15th, 1/e^4, and e^(4/8). The tutorial also demonstrates how to handle expressions with coefficients in the exponent, such as e^(natural log 2) and e^(1/2 natural log 7), by applying logarithmic properties and converting between exponential and logarithmic forms.

What is the first step in simplifying expressions using logarithmic properties?

• Convert the expression to a polynomial

• Use trigonometric identities

• Apply the quadratic formula

• Set the expression equal to a variable

What does the expression log base a of a to the power of x simplify to?

• 0

• a

• x

• 1

How can one divided by e to the 4th be expressed as a power of e?

• e to the power of 4

• e to the power of 0

• e to the power of -4

• e to the power of 1/4

Tags

CCSS.HSF.BF.B.5

What is the equivalent exponential form of natural log of e to the power of negative 4?

• e to the power of 4

• e to the power of -4

• e to the power of 0

• e to the power of 1

How do you convert the 8th root of e to the 4th into a rational exponent?

• e to the power of 2

• e to the power of 4/8

• e to the power of 8/4

• e to the power of 1/2

What is the simplified form of e to the power of natural log 2?

• 1

• 2

• 0

• e

What property is used to simplify e to the power of natural log 2?

• a to the power of log base a of x equals x

• a to the power of x equals log base a of x

• log base a of a to the power of x equals x

• x to the power of log base a of a equals x

How can you simplify e to the power of 1/2 natural log 7?

• 7

• 7 to the power of 1/2

• e to the power of 7

• 1/2

What is the first step in simplifying e to the power of 1/2 natural log 7?

• Apply the quadratic formula

• Convert to a polynomial

• Move the coefficient to the exponent position

• Use trigonometric identities

Tags

CCSS.HSF.BF.B.5

What is the equivalent form of e to the power of natural log of 7 to the 1/2?

• 7 to the power of 1/2

• 7

• e to the power of 7

• 1/2

Tags

CCSS.HSF.BF.B.5