Question

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

Answer 1

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