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Which logarithmic equation is equivalent to the exponential equation below?87.18 = eaA.log87.18 3.45 = eB.ln 87.18 = aC.ln a = 87.18D.loga 87.18 = 3.45

Which logarithmic equation is equivalent to the exponential equation below?87.18 = eaA-example-1
User Jonju
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1 Answer

14 votes
14 votes
Step-by-step explanation

We must find the equivalent expression to the logarithmic equation:


87.18=e^a.

We consider the following properties of logarithms:


\begin{gathered} \ln(x^a)=a\cdot\ln(x), \\ \ln(e)=1. \end{gathered}

(1) Taking the logarithm on both sides and using the first property, we have:


\ln(87.18)=a\cdot\ln(e).

(2) Using the second property, we get:


\begin{gathered} \ln(87.18)=a\cdot1, \\ \ln(87.18)=a. \end{gathered}Answer

B. ln 87.18 = a

User Vikhram
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