Exponential Form Calculator
Convert between exponential and logarithmic forms with step-by-step solutions
Exponential Form Conversions
Only positive integers can be converted to exponential form
Result
Step-by-Step Solution
Key Concepts
Exponential Form
Expressing numbers using exponents (e.g., 2³)
Prime Factorization
Breaking down numbers into prime factors
Log-Exponential Relation
log₍b₎(c) = a ⟺ b^a = c
Important Rules
Integers Only
Exponential form applies to positive integers
Prime Factors
Use smallest prime factors first
Base Restrictions
Logarithm base must be positive and ≠ 1
Inverse Operations
Logarithms and exponentials are inverses
Understanding Exponential Form
What is Exponential Form?
Exponential form is a way to express numbers using exponents. For integers, this means breaking the number down into its prime factors and representing repeated factors as powers.
Prime Factorization Process
- 1.Start with the smallest prime (2)
- 2.Divide repeatedly until no longer divisible
- 3.Move to next prime number
- 4.Continue until quotient is 1
Conversion Types
Number to Exponential
250 = 2 × 5³
Prime factorization method
Log to Exponential
log₂(8) = 3 → 2³ = 8
Using logarithm definition
Exponential to Log
3⁴ = 81 → log₃(81) = 4
Inverse relationship