# Video: Converting an Equation from Exponential to Logarithmic Form

Express 8^π₯ = π¦ in its equivalent logarithmic form.

01:14

### Video Transcript

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

In order to answer this question, weβll firstly look at the general rule that links exponents or indices and logarithms. If π to the power of π is equal to π₯, then log of π₯ to the base π is equal to π. In this general rule, the value of π is known as the base. π is known as the exponent, index, or power.

In this question, π, the base number, is eight. The exponent doesnβt have a single value. It is equal to π₯. In this example, the value π¦ is in the same place as π₯ in the general rule. Substituting in these three values gives us log π¦ to the base eight is equal to π₯.

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