Question

question 2 of 10
which logarithmic equation is equivalent to the exponential equation below?
87.18 = e^a
a. ln 87.18 = a
b. log_a 87.18 = 3.45
c. log_87.18 3.45 = e
d. ln a = 87.18

Explanation:

Step1: Recall the exponential - logarithmic conversion rule

The general rule for converting an exponential equation \(y = b^{x}\) to a logarithmic equation is \(\log_{b}y=x\). When the base \(b = e\), the logarithm is the natural logarithm, denoted as \(\ln\). So, if we have an exponential equation \(y = e^{x}\), it can be converted to the logarithmic equation \(\ln y=x\).

Step2: Apply the rule to the given equation

In the given exponential equation \(87.18 = e^{a}\), we can identify that \(y = 87.18\), \(b = e\), and \(x = a\). Using the conversion rule for natural logarithms (since \(b = e\)), we get \(\ln(87.18)=a\).

Answer:

A. \(\ln 87.18 = a\)