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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 Below8718 EaAlog8718 345 EBln 8718 ACln A 8718Dloga 8718 345 class=

Sagot :

Explanation

We must find the equivalent expression to the logarithmic equation:

[tex]87.18=e^a.[/tex]

We consider the following properties of logarithms:

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

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

[tex]\ln(87.18)=a\cdot\ln(e).[/tex]

(2) Using the second property, we get:

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

B. ln 87.18 = a

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