How Are Indices and Logarithm Related

Is there any relationship between Indices and Logarithm?

To those unknown, Indices and logarithm are closely related to each other.
Their difference lies in the way they are presented or in their format.

Indices format: a^x = y

Logarithm format: log_aY = x

How do we select the appropriate format to use?
Which format to use depends on the initial maths problem or questions given, and what is the unknown to be solved.

If all else is given and the power of a number / expression has to be determined, select the "Logarithm" format. Power (x) = log_aY ==> directly obtaining the power x.

If the base "a" and the power "x" is known, then the Indices format can be used.

Example of Real - life Application:
In digital electronics engineering (where the base is 2 due to only two numbers present, 0 & 1), when the designer has to know the number of stages (x) to represent a count cycle of 8, he applies the logarithm format. log₂8 = x

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