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:
An integer can be expressed as a product of primes through prime factorization. For example, 250 can be written as:
250 = 2 × 5 × 5 × 5 250 = 2 \times 5 \times 5 \times 5 250 = 2 × 5 × 5 × 5We can use the exponential form to express this more concisely:
250 = 2 × 5 3 250 = 2 \times 5^3 250 = 2 × 5 3We say that 2 × 5 3 2 \times 5^3 2 × 5 3 is the exponential form of 250 250 250 .
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!
❗ Exponential form and exponential notation are different. Exponential notation is similar to the exponential form but doesn't rely on prime factorization. Exponential notation is a way to represent any number in a more accessible format for calculations. Head to our exponential notation calculator to learn more.
A logarithmic number can be converted into its corresponding exponential form due to their relation:
b a = c ⟹ log b c = a e a = c ⟹ ln c = a b^a = c \ \Longrightarrow \ \log_b c = a\\[0.5em] e^a = c \ \Longrightarrow \ \ln c = a\\
b a = c ⟹ lo g b c = a e a = c ⟹ ln c = a
🙋 To learn more about logarithms, visit our log calculator.
For example, consider ln 15 = 2.71 \ln 15 = 2.71 ln 15 = 2.71 . We can convert to exponential form by raising e e e to both sides:
ln 15 ≈ 2.71 ⇒ e ln 15 = e 2.71 15 = e 2.71 \begin \ln 15 &\approx 2.71\\ \Rightarrow e^ <\ln 15>&= e^\\ 15 &= e^ \end ln 15 ⇒ e l n 15 15 ≈ 2.71 = e 2.71 = e 2.71
Consider another example, log 2 8 = 3 \log_2 8 = 3 lo g 2 8 = 3 , which we can convert by raising 2 2 2 to both sides:
log 2 8 = 3 ⇒ 2 log 2 8 = 2 3 8 = 2 3 \begin \log_2 8 &= 3\\ \Rightarrow 2^ <\log_2 8>&= 2^\\ 8 &= 2^ \end lo g 2 8 ⇒ 2 l o g 2 8 8 = 3 = 2 3 = 2 3
Calculating exponential to logarithm form is basically the inverse of what we did in the last section.
log b c = a ⟹ b a = c ln c = a ⟹ e a = c \begin
For example, consider 2 5 = 32 2^5 = 32 2 5 = 32 , which we can convert by applying log 2 \log_2 lo g 2 on both sides:
2 5 = 32 ⇒ log 2 ( 2 5 ) = log 2 32 5 = log 2 32 \begin 2^5 &= 32\\ \Rightarrow \log_2(2^5) &= \log_232\\ 5 &= \log_2 32 \end 2 5 ⇒ lo g 2 ( 2 5 ) 5 = 32 = lo g 2 32 = lo g 2 32
Our exponential form calculator is straightforward to use:
The exponential form of 128 = 2 7 . To find this answer, follow these steps:
The exponential form of 3×3×3×3 = 3 4 . To arrive at this answer, follow these simple steps:
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 × 10 1 , 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 logb(c) = a, and vice versa.