Answer
1)
The exponential form: $5^{1}=5$
The logarithmic form: $\log_{5}5=1$.
2)
The exponential form: $4^{-2}=\frac{1}{16}$
The logarithmic form: $\log_{4}\frac{1}{16}=-2$.
3)
The exponential form: $4^{2}=16$
The logarithmic form: $\log_{4}16=2$.
4)
The exponential form: $10^{4}=10,000$
The logarithmic form: $\log_{10}10,000=4$.
5)
The exponential form: $3^{3}=27$
The logarithmic form: $\log_{3}27=3$.
6)
The exponential form: $7^{0}=1$
The logarithmic form: $\log_{7}0=1$
Work Step by Step
The definition of the logarithm function can be translated into mathematical formulas such as the following. The given expressions are equivalent.
The exponential form: $b^{x}=a$
The logarithmic form: $\log_{b}a=x$.
Here, we have to translate the given expressions to the exponential form:
1)
The exponential form: $5^{1}=5$
The logarithmic form: $\log_{5}5=1$.
2)
The exponential form: $4^{-2}=\frac{1}{16}$
The logarithmic form: $\log_{4}\frac{1}{16}=-2$.
3)
The exponential form: $4^{2}=16$
The logarithmic form: $\log_{4}16=2$.
4)
The exponential form: $10^{4}=10,000$
The logarithmic form: $\log_{10}10,000=4$.
5)
The exponential form: $3^{3}=27$
The logarithmic form: $\log_{3}27=3$.
6)
The exponential form: $7^{0}=1$
The logarithmic form: $\log_{7}0=1$
