4. Prove that the logarithm of unity to any non-zero base.is zero.
Answers
The logarith "of a number" is the power to which you raise a base, in order to get that number.
For example, we know that 2^4 = 16
Therefore, by definition of "logarithm", the log in base 2 of 16 is 4
log2(16) = 4
Go back to rule of exponents:
When multiplying powers of a base, add the powers
a^3 * a^5 = a^(3+5) = a^8
When dividing powers, subtract the powers
(a^7) / (a^5) = a^(7-5) = a^2
What happens when you divide something by itself? you get 1.
(a^3)/(a^3) = 1
and we know:
(a^3)/(a^3) = a^(3-3) = a^0
And the value of a does not matter (as long as a is not zero).
For for all bases "b" (any positive number used as a base for logarithms),
b^0 is ALWAYS equal to 1
Therefore, the logarithm of 1, in any base "b", must always be zero.
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Logarithms are used with other "things" than normal numbers.
For normal numbers, "unity" is always 1.
For other "things", unity could mean something else, that looks different from a "1", but still works like a "1".
In order to prepare you for higher mathematics, they are trying to get you used to the word "unity".
For normal numbers, it simply means "1".Answer:
Step-by-step explanation: