Converting Logarithms and Exponentials

Front

Write in exponential form: log₃ 6561 = 8

Back

3⁸ = 6561

Front

What is the natural logarithm of a number?

Back

The natural logarithm (LN) is the logarithm to the base 'e', where 'e' is approximately equal to 2.718.

Front

Convert logₑ x = y to exponential form.

Back

x = e^y

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation.

Front

Write in exponential form: log₄ 256 = 4

Back

4⁴ = 256

Front

What is the common logarithm?

Back

The common logarithm is the logarithm to the base 10, often written as log(x).

Front

Convert log₁₀ 100 = 2 to exponential form.

Back

10² = 100

Front

What does logₐ b = c mean?

Back

It means that a raised to the power of c equals b (a^c = b).

Front

Write in exponential form: log₂ 32 = 5

Back

2⁵ = 32

Front

What is the base of the natural logarithm?

Back

The base of the natural logarithm is 'e'.