Answer
1)
The exponential form: $4^{3}=64$
The logarithmic form: $\log_{4}64=3$.
2)
The exponential form: $10^{-1}=0.1$
The logarithmic form: $\log_{10}0.1=-1$.
3)
The exponential form: $2^{8}=256$
The logarithmic form: $\log_{2}256=8$.
4)
The exponential form: $5^{0}=1$
The logarithmic form: $\log_{5}1=0$.
5)
The exponential form: $0.5^{2}=0.25$
The logarithmic form: $\log_{0.5}0.25=2$.
6)
The exponential form: $6^{-2}=\frac{1}{36}$
The logarithmic form: $\log_{6}\frac{1}{36}=-2$
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 logarithmic form:
1)
The exponential form: $4^{3}=64$
The logarithmic form: $\log_{4}64=3$.
2)
The exponential form: $10^{-1}=0.1$
The logarithmic form: $\log_{10}0.1=-1$.
3)
The exponential form: $2^{8}=256$
The logarithmic form: $\log_{2}256=8$.
4)
The exponential form: $5^{0}=1$
The logarithmic form: $\log_{5}1=0$.
5)
The exponential form: $0.5^{2}=0.25$
The logarithmic form: $\log_{0.5}0.25=2$.
6)
The exponential form: $6^{-2}=\frac{1}{36}$
The logarithmic form: $\log_{6}\frac{1}{36}=-2$
