6.3 Logarithmic functions  (Page 5/9)

What is a base $b$ logarithm? Discuss the meaning by interpreting each part of the equivalent equations $b^y=x$ and ${\log }_{b}x=y$ for $b>0,b\ne 1.$

How is the logarithmic function $f(x)={\log }_{b}x$ related to the exponential function $g(x)=b^x?$ What is the result of composing these two functions?

How can the logarithmic equation ${\log }_{b}x=y$ be solved for $x$ using the properties of exponents?

Discuss the meaning of the common logarithm. What is its relationship to a logarithm with base $b,$ and how does the notation differ?

Discuss the meaning of the natural logarithm. What is its relationship to a logarithm with base $b,$ and how does the notation differ?

${\text{log}}_4(q)=m$

${\text{log}}_a(b)=c$

${\log }_{16}\left(y\right)=x$

${\log }_x\left(64\right)=y$

${\log }_y\left(x\right)=\mathrm{-11}$