Video: Converting an Equation from Exponential to Logarithmic Form

Express 8^π‘₯ = 𝑦 in its equivalent logarithmic form.

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Video Transcript

Express eight to the power of π‘₯ equals 𝑦 in its equivalent logarithmic form.

In order to answer this question, we’ll firstly look at the general rule that links exponents or indices and logarithms. If π‘Ž to the power of 𝑛 is equal to π‘₯, then log of π‘₯ to the base π‘Ž is equal to 𝑛. In this general rule, the value of π‘Ž is known as the base. 𝑛 is known as the exponent, index, or power.

In this question, π‘Ž, the base number, is eight. The exponent doesn’t have a single value. It is equal to π‘₯. In this example, the value 𝑦 is in the same place as π‘₯ in the general rule. Substituting in these three values gives us log 𝑦 to the base eight is equal to π‘₯.

We can therefore conclude that eight to the power of π‘₯ equals 𝑦, in its equivalent logarithmic form, is log 𝑦 to the base eight equals π‘₯.

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