Question

question 11/24
11 write the following exponential equation in log form. $3^{-3} = \frac{1}{27}$
a $\log_{3} \frac{1}{27} = -3$
b $\log_{27} 3 = -3$
c $\log_{\frac{1}{3}} 3 = -3$
d $\log_{\sqrt{3}} \frac{1}{27} = 3$

Explanation:

Step1: Recall the logarithmic definition

The exponential form \(a^b = c\) can be converted to logarithmic form as \(\log_a c = b\).

Step2: Apply the definition to the given equation

Given the exponential equation \(3^{-3}=\frac{1}{27}\), here \(a = 3\), \(b=- 3\) and \(c=\frac{1}{27}\).
Using the conversion formula \(\log_a c=b\), we substitute the values: \(\log_3\frac{1}{27}=-3\).

Answer:

A. \(\log_{3}\frac{1}{27}=-3\)