Express the following equations in logarithmic form:

(a) [tex]$5^5 = 3125$[/tex] is equivalent to the logarithmic equation: [tex]$\log_5 3125 = \square$[/tex]

(b) [tex]$10^{-2} = 0.01$[/tex] is equivalent to the logarithmic equation: [tex]$\log_{10} 0.01 = \square$[/tex]

Sure, let's express the given exponential equations in their equivalent logarithmic form.

When we have an equation in the form [tex]$ a^b = c $[/tex], we can write it in logarithmic form as [tex]$ \log_a(c) = b $[/tex]. Here, the base [tex]$ a $[/tex] of the exponential becomes the base of the logarithm, the exponent [tex]$ b $[/tex] becomes the result of the logarithm, and the result [tex]$ c $[/tex] of the exponential becomes the number we are taking the logarithm of.

Let's apply this to the two given equations:

(a) [tex]$ 5^5 = 3125 $[/tex]

Using the logarithmic form:
- Base of the exponential is 5.
- Exponent is 5.
- Result is 3125.

So the logarithmic form of this equation is [tex]$\log_5(3125) = 5$[/tex].

(b) [tex]$ 10^{-2} = 0.01 $[/tex]

Using the logarithmic form:
- Base of the exponential is 10.
- Exponent is -2.
- Result is 0.01.

So the logarithmic form of this equation is [tex]$\log_{10}(0.01) = -2$[/tex].

Therefore, the logarithmic forms are:

(a) [tex]$\log_5(3125) = 5$[/tex]

(b) [tex]$\log_{10}(0.01) = -2$[/tex]

These are the equivalent logarithmic equations for the given exponential equations.

Express the following equations in logarithmic form:(a) [tex]\(5^5 = 3125\)[/tex] is equivalent to the logarithmic equation: [tex]\(\log_5 3125 = \square\)[/tex](b) [tex]\(10^{-2} = 0.01\)[/tex] is equivalent to the logarithmic equation: [tex]\(\log_{10} 0.01 = \square\)[/tex]

Answer :

Other Questions

Express the following equations in logarithmic form:

(a) [tex]\(5^5 = 3125\)[/tex] is equivalent to the logarithmic equation: [tex]\(\log_5 3125 = \square\)[/tex]

(b) [tex]\(10^{-2} = 0.01\)[/tex] is equivalent to the logarithmic equation: [tex]\(\log_{10} 0.01 = \square\)[/tex]