Converting Between Logarithms and Exponents

What is the relationship between logarithms and exponents?

• They are both functions of multiplication.

• They are unrelated.

• They are inverses of each other.

• They are the same.

If 3 to the power of 7 equals 2187, how is this written in logarithmic form?

• log base 3 of 2187 equals 7

• log base 7 of 3 equals 2187

• log base 7 of 2187 equals 3

• log base 2187 of 3 equals 7

If 5 to the power of 3 equals 125, how is this expressed in logarithmic form?

• log base 5 of 125 equals 3

• log base 3 of 125 equals 5

• log base 125 of 3 equals 5

• log base 125 of 5 equals 3

What does log base 6 of 216 equals 3 convert to in exponential form?

• 3 to the power of 6 equals 216

• 6 to the power of 216 equals 3

• 216 to the power of 6 equals 3

• 6 to the power of 3 equals 216

Convert log base 9 of 729 equals 3 to exponential form.

• 729 to the power of 9 equals 3

• 9 to the power of 729 equals 3

• 3 to the power of 9 equals 729

• 9 to the power of 3 equals 729

What does a common logarithm imply when no base is written?

• Base 10

• Base 5

• Base 6

• Base 2

What is the value of log base 10 of 10?

• 100

• 0

• 1

• 10

Calculate the value of log base 5 of 625.

• 5

• 4

• 3

• 6

What is the exponential form of log base 2 of 1/2 equals -1?

• 1/2 to the power of 2 equals -1

• 2 to the power of -1 equals 1/2

• 1/2 to the power of -1 equals 2

• 2 to the power of 1/2 equals -1

If log base 3 of 1 equals 0, what does this imply in exponential form?

• 3 to the power of 1 equals 0

• 0 to the power of 3 equals 1

• 1 to the power of 3 equals 0

• 3 to the power of 0 equals 1