Logarithms can be considered as the inverse of exponents (or indices).
Definition of Logarithm
If ax = y such that a > 0, a ≠ 1 then loga y = x
ax = y ↔ loga y = x
Exponential Form
y = ax
Logarithmic Form
loga y = x
Remember: The logarithm is the exponent.
The following diagram shows the relationship between logarithm and exponent. Scroll down the page for more examples and solutions for logarithms and exponents.Example:
Convert the following exponential form to the logarithmic form:
a) 42 = 16
b) 25 = 32
c)
Solution:
a) 42 = 16
2 = log4 16 (the log is the exponent)
b) 25 = 32
5 = log2 32
Example:
Convert the following logarithmic form to exponential form
a) 3 = log2 8
b) 2 = log5 25
c)
Solution:
a) 3 = log2 8
23 = 8
b) 2 = log5 25
52 = 25
Take note of the following:
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