Logarithmic Form

Logarithmic Form

How to write equations in exponential form to logarithmic form and vice versa: definition, examples, and their solutions.

Definition

Logarithm is a way to write the exponent of a number.

Logarithm is a way
to write the [exponent] of a number.

For 20 = 1,
the exponent is 0.
So 0 = log2 1.

For 21 = 2,
the exponent is 1.
So 1 = log2 2.

By the same way,
for 2[blue] = 3,
the exponent is [blue].
So [blue] = log2 3.

[log2 3] is read as [log base 2 of 3].

Example 1: Logarithmic Form of 24 = 16

Write the given equation in logarithmic form. 2^4 = 16

24 = 16
The exponent is 4.

So 4 = log2 16.

Example 2: Logarithmic Form of 3-2 = 1/9

Write the given equation in logarithmic form. 3^-2 = 1/9

3-2 = 1/9
The exponent is -2.

So -2 = log3 (1/9).

Negative exponent

Example 3: Logarithmic Form of 51/2 = √5

Write the given equation in logarithmic form. 5^(1/2) = sqrt(5)

51/2 = √5
The exponent is 1/2.

So 1/2 = log55.

Rational exponents

Example 4: Exponential Form of 2 = log3 9

Write the given equation in exponential form. 2 = log_3 9

2 = log3 9
The exponent is 2.

So 32 = 9.

Example 5: Exponential Form of -5 = log2 (1/32)

Write the given equation in exponential form. -5 = log_2 (1/32)

-5 = log2 (1/32)
The exponent is -5.

So 2-5 = 1/32.

Example 6: Exponential Form of 2/3 = log7 349

Write the given equation in exponential form. 2/3 = log_7 [cube root(49)]

2/3 = log7 349
The exponent is 2/3.

So 72/3 = 349.