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When you write logarithm of 1 with base b = x, through logarithm properties, that would be x to the power of b equals 1.
Now, from the law of exponents, any number raised to the power of zero is 1. Thus logarithm of 1 with base b is truly zero.
Now, from the law of exponents, any number raised to the power of zero is 1. Thus logarithm of 1 with base b is truly zero.