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Match each equation on the left with its equivalent logarithmic form. (2 points) NER 2 (e3t) 12 1 1 12 (e3t) = 2 111 HR JE M 1 HUN 3 (ezt) = 12 :: 3t = log 6 :: 2t = log, 4 loge

Respuesta :

Let's solve each equation to find the right match.

[tex]2(e^{3t})=12[/tex]

First, we divide the equation by 2.

[tex]\begin{gathered} \frac{2(e^{3t})}{2}=\frac{12}{2} \\ e^{3t}=6 \end{gathered}[/tex]

Then, we apply logarithms on each side.

[tex]\begin{gathered} \log _e(e^{3t})=\log _e(6) \\ 3t=\log _e(6) \end{gathered}[/tex]

So the first expression matches the first answer choice.

The second equation is

[tex]12(e^{3t})=2[/tex]

First, we divide the equation by 12.

[tex]\begin{gathered} \frac{12(e^{3t})}{12}=\frac{2}{12} \\ e^{3t}=\frac{1}{6} \end{gathered}[/tex]

Then, we apply logarithms on each side.

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