Understanding Exponential and Logarithmic Equations

The video tutorial explains how to convert exponential equations into logarithmic form. It begins by establishing the equivalence between exponential and logarithmic equations, using the formula log base B of N equals A, which means B raised to the power of A equals N. The tutorial then provides examples, such as converting 10^3 = 1000 and 10^-2 = 100 into logarithmic form, emphasizing the concept of common logs where the base 10 is omitted.

What does the equation log base b of n = a imply in terms of exponential form?

• a raised to the power of b equals n

• n raised to the power of b equals a

• b raised to the power of n equals a

• b raised to the power of a equals n

In the equation 10^3 = 1,000, what is the base in the corresponding logarithmic form?

• 10

• 3

• None of the above

• 1,000

What is the exponent in the logarithmic form of the equation 10^3 = 1,000?

• None of the above

• 10

• 3

• 1,000

When converting 10^3 = 1,000 to logarithmic form, what is the number?

• 1,000

• 10

• None of the above

• 3

What is a common logarithm?

• A logarithm with base 1

• A logarithm with base 2

• A logarithm with base 10

• A logarithm with base e

In the equation 10^-2 = 100, what is the exponent in the logarithmic form?

• -2

• None of the above

• 10

• 100

What is the number in the logarithmic form of the equation 10^-2 = 100?

• None of the above

• -2

• 100

• 10

Why do we leave off the base in a common logarithm?

• Because it is always base 1

• Because it is always base 10

• Because it is always base 2

• Because it is always base e