Video: Converting an Equation from Exponential to Logarithmic Form

Express 4⁻² = 1/16 in its equivalent logarithmic form.

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Video Transcript

Express four to the power of negative two equals one 16th in its equivalent logarithmic form.

Let’s firstly consider how we can write the general form π‘₯ equals π‘Ž to the power of 𝑛 in logarithmic form. In this case, π‘Ž is known as the base number and 𝑛 is our exponent, index, or power. The equivalent logarithmic form to this is log π‘₯ to the base π‘Ž is equal to 𝑛.

In our example, four to the power of negative two equals one 16th. Then, π‘Ž is equal to four. The exponent 𝑛 is equal to negative two. And the value of π‘₯ is one over 16 or one 16th. Substituting in these three values gives us log of one 16th to the base four is equal to negative two. This is the equivalent logarithmic form of four to the power of negative two equals one 16th.

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