Question

which logarithmic equation is equivalent to the exponential equation below?
$3^c = 27$

a. $log_c 27 = 3$

b. $log_3 27 = c$

c. $log_{27} c = 3$

d. $log_3 c = 27$

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The general formula for converting an exponential equation \(a^{x}=y\) (where \(a>0,a
eq1\)) to a logarithmic equation is \(\log_{a}y = x\).

Step2: Identify the values of \(a\), \(x\), and \(y\) from the given exponential equation

In the given exponential equation \(3^{c}=27\), we have:

• The base \(a = 3\) (the base of the exponential function).
• The exponent \(x = c\) (the power to which the base is raised).
• The result \(y = 27\) (the value of the exponential expression).

Step3: Apply the conversion formula

Using the formula \(\log_{a}y=x\) with \(a = 3\), \(x = c\), and \(y = 27\), we get \(\log_{3}27=c\).

Answer:

B. \(\log_{3}27 = c\)