Logarithms Calculator

Expand (For other logarithm calculations involving numbers, visit our logarithm calculator



Evaluate the answer of the logarithmic expression Base 0

Using a base of b and a power of n, the logarithmic equation is:
bn = 1

Plugging in the numbers you entered and solving, we get:
Base 0 =
Base 0 = 1 Using the logarithmic equation, determine what base raised to a power of equals .

log ??? =

Let's call our missing base b. Therefore, our logarithmic equation becomes:
b =

We need to isolate b, so we take the Natural Log (described later) of both sides. We get:
Ln(b) = Ln()

One of the logarithmic identities states the following:
Ln(bn) = n * Ln(b)

Using this, we rewrite our logarithimic equation below:
* Ln(b) = Ln() <--- Using our logartithmic identity above

Next, we divide both sides of the equation by to isolate b:
Ln(b) =Ln()

The natural log, denoted Ln, is a special type of log that uses a base named e.
e = 2.

Ln() is what power we have to raise e to in order to get .

Using a calculator or guess and check method, we simplify our equation:
Ln(b) =

Ln(b) =

Another logarithmic identity states the following:
eLn(b) = b

Using this, we rewrite our logarithimic equation below:
eLn(b) = e
b = 2.() <--- Using our 2nd logartithmic identity above
b = 1 Using the logarithmic equation, determine what power 2. needs to be raised to in order to get .
log 2. = ???

Let's call our missing power n. Therefore, our logarithmic equation becomes:
log 2. = n

Expressing this in logarithmic terms, we get:
2.n =

We need to isolate n, so we take the Natural Log (described later) of both sides. We get:
Ln() = Ln(2.n)

One of the logarithmic identities states the following:
Log(bn) = n * Log(b)

Using this, we rewrite our logarithimic equation below:
Ln() = n * Ln(2.) <--- Using our logartithmic identity above

Next, we divide both sides of the equation by Ln(2.) to isolate n:
n =Ln()
Ln(2.)

The natural log, denoted Ln, is a special type of log that uses a base named e.
e = 2.

Ln() is what power we have to raise e to in order to get .
Ln(2.) is what power we have to raise e to in order to get 2..

Using a calculator or guess and check method, we simplify and solve for n:
n =
1

In mathematical terms, this means base 2.0 = .

In logarithmic terms, we now have:
2. = 0