write the equation in its equivalent logarithmic form.\n\n3^{-5}=\\frac{1}{243}\n\nthe logarithmic form is…

write the equation in its equivalent logarithmic form.\n\n3^{-5}=\\frac{1}{243}\n\nthe logarithmic form is \n(use integers or fractions for any numbers in the expression.)

write the equation in its equivalent logarithmic form.\n\n3^{-5}=\\frac{1}{243}\n\nthe logarithmic form is \n(use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall the conversion formula

The formula for converting an exponential equation (a^b = c) to a logarithmic equation is (\log_a c=b).

Step2: Identify the values of (a), (b), and (c)

In the given equation (3^{-5}=\frac{1}{243}), we have (a = 3), (b=-5), and (c=\frac{1}{243}).

Step3: Apply the conversion formula

Substituting the values into the formula (\log_a c=b), we get (\log_3\frac{1}{243}=-5).

Answer:

(\log_3\frac{1}{243}=-5)