Express 243 to the power of one-fifth equals three in its equivalent logarithmic form.
Let’s firstly consider our general rule that converts indices or exponents to logarithms. If 𝑥 is equal to 𝑎 to the power of 𝑛, where 𝑎 is the base number and 𝑛 is the exponent, index, or power, then we know that log of 𝑥 to the base 𝑎 is equal to 𝑛.
In this specific question, 243 to the power of one-fifth equals three. Then 𝑎 is equal to 243. The exponent 𝑛 is equal to one-fifth, and the value of 𝑥 equals three. Substituting in these three values gives us log of three to the base 243 equals one-fifth. This is the equivalent logarithmic form of 243 to the power of one-fifth is equal to three.