Logarithmic Form
How to change an equation in exponent form to logarithmic form (and vice versa): definition, 6 examples, and their solutions.
Definition
A logarithm (log) is a way
to write the exponent.
For example,
if 2[exponent] = 3,
then the exponent is log2 3.
log2 3 is read as
[log base 2 of 3].
Example24 = 16 → Logarithmic Form
24 = 16
The exponent is 4.
So 4 = log2 16.
So
4 = log2 16
is the answer.
Example3-2 = 1/9 → Logarithmic Form
3-2 = 1/9
The exponent is -2.
So -2 = log3 1/9.
Negative Exponent
So
-2 = log3 1/9
is the answer.
Example51/2 = √5 → Logarithmic Form
51/2 = √5
The exponent is 1/2.
So 1/2 = log5 √5.
Rational Exponent
So
1/2 = log5 √5
is the answer.
Example2 = log3 9 → Exponential Form
2 = log3 9
The exponent is 2.
The base is 3.
So 32 = 9.
So
32 = 9
is the answer.
Example-5 = log2 1/32 → Exponential Form
-5 = log2 1/32
The exponent is -5.
The base is 2.
So 2-5 = 1/32.
So
2-5 = 1/32
is the answer.
Example2/3 = log7 3√49 → Exponential Form
2/3 = log7 3√49
The exponent is 2/3.
The base is 7.
So 72/3 = 3√49.
So
72/3 = 3√49
is the answer.