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Question

Evaluate:

(i) log100.01

(ii) log2(1÷8)

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Solution

(i)

l e t space log subscript 10 0.01 equals x rightwards double arrow 10 to the power of x equals 0.01 rightwards double arrow 10 to the power of x equals 10 to the power of negative 2 end exponent x equals negative 2 space log subscript 10 0.01 equals negative 2

(ii)

l e t space log subscript 2 open parentheses 1 over 8 close parentheses equals x rightwards double arrow 2 to the power of x equals 1 over 8 rightwards double arrow 2 to the power of x equals 2 to the power of negative 3 end exponent x equals negative 3 rightwards double arrow space log subscript 2 open parentheses 1 over 8 close parentheses equals negative 3


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