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Express four to the power of negative two equals one 16th in its equivalent logarithmic form.
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Letβs firstly consider how we can write the general form π₯ equals π to the power of π in logarithmic form.
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In this case, π is known as the base number and π is our exponent, index, or power.
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The equivalent logarithmic form to this is log π₯ to the base π is equal to π.
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In our example, four to the power of negative two equals one 16th.
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Then, π is equal to four.
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The exponent π is equal to negative two.
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And the value of π₯ is one over 16 or one 16th.
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Substituting in these three values gives us log of one 16th to the base four is equal to negative two.
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This is the equivalent logarithmic form of four to the power of negative two equals one 16th.