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Answer :
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.
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.
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