Question Video: Rewriting a Logarithmic Equation in Exponential Form

Write the logarithmic equation 8 = ln 𝑥 in exponential form.

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Video Transcript

Write the logarithmic equation eight equals ln of 𝑥 in exponential form.

In this question, we are given the natural logarithm ln of 𝑥. We know that the natural logarithm ln of 𝑥 is equal to log of base 𝑒 of 𝑥. We also know that ln is the inverse function of the exponential function. If 𝑦 is equal to ln of 𝑥, then 𝑒 to the power of 𝑦 equals 𝑥. In this question, eight is equal to ln of 𝑥. This means that 𝑒 to the power of eight or 𝑒 to the eighth power is equal to 𝑥. The logarithmic equation eight equals ln 𝑥 written in exponential form is 𝑒 to the power of eight equals 𝑥.

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