Video: Converting an Equation from Exponential to Logarithmic Form

Video Transcript

Express eight to the power of 𝑥 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 𝑎 to the power of 𝑛 is equal to 𝑥, then log of 𝑥 to the base 𝑎 is equal to 𝑛. In this general rule, the value of 𝑎 is known as the base. 𝑛 is known as the exponent, index, or power.

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

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