Exponential Form Calculator

Whether you wish to write an integer in exponential form or convert a number from log to exponential format, our exponential form calculator can help you.

In mathematics, we say a number is "in exponential form" when one or more exponents are involved. In the article below, we will briefly discuss the following fundamentals to ease you into the subject further:

• Writing integers in exponential form;
• Calculating log to exponential form conversion; and
• Calculating exponential to logarithm form.

An integer can be expressed as a product of primes through prime factorization. For example, 250 can be written as:

We can use the exponential form to express this more concisely:

We say that $2 \times 5^3$ is the exponential form of $250$.

Writing the number in the exponential form retains the vital information (the prime factors) while saving space. If you want to learn how to prime factorize a number, head to our prime factorization calculator.

Since we depend on prime factorizing to write a number this way, we can only express non-zero whole numbers in the exponential form. And of course, since prime numbers' only factors are themselves, their prime factorizations are themselves, too!

A logarithmic number can be converted into its corresponding exponential form due to their relation:

where:

• $b$ — The base;
• $a$ — The exponent;
• $c$ — A number; and
• $e$ — Euler's number.

For example, consider $\ln 15 = 2.71$. We can convert to exponential form by raising $e$ to both sides:

Consider another example, $\log_2 8 = 3$, which we can convert by raising $2$ to both sides:

Calculating exponential to logarithm form is basically the inverse of what we did in the last section.

For example, consider $2^5 = 32$, which we can convert by applying $\log_2$ on both sides:

Our exponential form calculator is straightforward to use:

1. Select what conversion you wish to perform. You can ask our calculator to:

   • Write the exponential form of a whole number;
   • Convert log to exponential form; or
   • Convert exponential to log form.

2. Enter the whole number you wish to convert to exponential form, and our calculator will do the rest.

3. To convert from log form to exponential form ($\log_bc =a \Longrightarrow b^a=c$):

   • Enter the logarithm base (b) along with the number (c). The calculator converts it to exponential form and gives you the result.

   • Tip: If base $b = e$, enter e in the field.

4. To convert from exponential form to log form ($b^a=c \Longrightarrow \log_bc = a$) to log form:

   • Enter the base (b) along with the exponent (a). Our tool will calculate the logarithm form from the exponential form.

   • Tip: If base $b = e$, enter e in the field.

The exponential form of 128 = 2⁷. To find this answer, follow these steps:

1. Prime factorize the number: 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2.
2. Find the exponent of the prime factor 2. Since 2 is multiplied 7 times, the exponent is 7.
3. Write the number in the form factor^exponent to get: 128 = 2⁷
4. Verify the result with our exponential form calculator.

The exponential form of 3×3×3×3 = 3⁴. To arrive at this answer, follow these simple steps:

1. Count the number of times the prime factor 3 is multiplied with itself to get the exponent 4.
2. Write the number in the form factor^exponent to get: 3⁴.
3. Verify with our exponential form calculator.

You cannot write 24.65 in the exponential form since it is not a whole number. You can, however, write it in the exponential notation 2.465 × 10¹, which is different from the exponential form. To learn how to do this, visit our exponential notation calculator.

A logarithm and an exponential function with the same base are inverse functions of each other. If b^a = c, then log_b(c) = a, and vice versa.