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Logarithm of 1

For any base b (as long as b is greater than and not equal to ), the logarithm of 1 is always 0.

That’s because any number raised to the power of 0 equals 1.

We can write this as:

Evaluate

Section titled “Evaluate ”
  • because
  • Answer:

Evaluate

Section titled “Evaluate ”
  • because
  • Answer:

Evaluate

Section titled “Evaluate ”
  • because
  • Answer:

Evaluate

Section titled “Evaluate ”
  • because
  • Answer:

Evaluate

Section titled “Evaluate ”
  • is undefined because we can’t find the logarithm of a negative base.
  • Answer: undefined

Find the value of such that

Section titled “Find the value of such that ”
  • because
  • Answer:

Natural logarithms of

Section titled “Natural logarithms of ”

Because we can rewrite as , we can evaluate it using the same principle.

We know that because .

So .

Solve for :

Section titled “Solve for : ”
  • because
  • Answer: