Solve for Exponents Calculator



Solve for Exponents Calculator helps solving for Exponents.

What is Exponentiation?

Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n.

When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bⁿ is the product of multiplying the number b n times.

How to solve for exponents?

For Xⁿ = Y:

Solve for n by taking the ln of both sides of the equation:

ln Xⁿ = ln Y

By identity we get:

n ^. ln X = ln Y

Dividing both sides by ln X:

n = ln Y / ln X

What does Solve for Exponents Calculator?

The Solve for Exponents Calculator calculator will solve for the exponent n in the exponential equation Xⁿ = Y, stated X raised to the nth power equals Y.

X = ?

Y = ?



Solve for Exponents Calculator - Examples

If you solve the following example, using Solve for Exponents Calculator you will find:

For 5ⁿ = 3:

Solve for n by taking the ln of both sides of the equation:

ln 5ⁿ = ln 3

By identity we get:

n ^. ln 5= ln 3

Dividing both sides by ln 5:

n = ln 3 / ln 5 =

= 1.6094379127059 / 1.0986122888536 =

= 1.4649735207179



If you solve the following example, using Solve for Exponents Calculator you will find:

For 6ⁿ = 4:

Solve for n by taking the ln of both sides of the equation:

ln 6ⁿ = ln 4

By identity we get:

n ^. ln 6= ln 4

Dividing both sides by ln 6:

n = ln 4 / ln 6 =

= 1.7917594695306 / 1.386294361354 =

= 1.2924812503606



If you solve the following example, using Solve for Exponents Calculator you will find:

For 7ⁿ = 5:

Solve for n by taking the ln of both sides of the equation:

ln 7ⁿ = ln 5

By identity we get:

n ^. ln 7= ln 5

Dividing both sides by ln 7:

n = ln 5 / ln 7 =

= 1.9459101493839 / 1.6094379127059 =

= 1.2090619551222