Question

Use the properties of logarithms to determine the value of logb 1. Explain your reasoning.

Answer 1

logb 1 = 0

Explanation:

Suppose that logb 1 = x.

Using the definition of a logarithm, bx = 1.

The only way a number that’s not equal to 1 can be raised to a power and equal 1 is if the exponent is 0. So, x = 0.

Therefore, logb 1 = 0.

Answer 2

`log_b 1 = 0`

Explanation:

Given

`log_b 1`

Required

Solve

`log_b 1`

Express 1 as
`b^0`

`log_b 1 = log_b b^0`

Apply power rule of logarithms

`log_b 1 = 0 * log_b b`

Multiply by 0

`log_b 1 = 0`