Video: Converting from Exponential to Logarithmic Form

Express 243^(1/5) = 3 in its equivalent logarithmic form.

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Video Transcript

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 π‘₯ is equal to π‘Ž to the power of 𝑛, where π‘Ž is the base number and 𝑛 is the exponent, index, or power, then we know that log of π‘₯ to the base π‘Ž is equal to 𝑛.

In this specific question, 243 to the power of one-fifth equals three. Then π‘Ž is equal to 243. The exponent 𝑛 is equal to one-fifth, and the value of π‘₯ 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.

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