### Video Transcript

Express log base 20 of 𝑧 equals one-half in its equivalent exponential form.

In order to answer this question, we recall that if log to the base 𝑎 of 𝑥 is equal to 𝑏, then 𝑥 is equal to 𝑎 to the power of 𝑏. In this question, our base 𝑎 is equal to 20. The value of 𝑏 is one-half. The variable 𝑥 is the variable 𝑧. This means that 𝑧 is equal to 20 to the power of one-half.

We recall that when any number is raised to an exponent of one-half, this is the same as square rooting the number. 20 to the power a half could therefore be rewritten as the square root of 20 or root 20. In its simplest form, this simplifies to two root five.

Any expression in logarithmic form can be converted to its equivalent exponential form using this rule.