Question Video: Rewriting an Exponential Equation in Logarithmic Form Mathematics

Write the exponential equation 𝑒^π‘₯ = 5 in logarithmic form.

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Video Transcript

Write the exponential equation 𝑒 to the π‘₯ power equals five in logarithmic form.

So exponential form is 𝑒 to the π‘Ž power equals 𝑏, whereas logarithmic form is log base 𝑒 of 𝑏 equals π‘Ž. And the great thing is we can go back and forth between these forms.

So we had the exponential equation 𝑒 to the π‘₯ equals five. So π‘Ž is equal to π‘₯ and 𝑏 is equal to five. So we have log base 𝑒 and 𝑏 should be five and π‘Ž should be equal to π‘₯. So here’s our equation.

However, we can reduce this because log base 𝑒 is actually the natural log. So we have that the natural log of five is equal to π‘₯.

Therefore, π‘₯ equals the natural log of five will be our final answer.

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