Consider the function $F\left(x\right)=2^x$F(x)=2x.
Graph the function.
Add the line $y=x$y=x to the graph.
By reflecting points on the curve $F\left(x\right)=2^x$F(x)=2x over the line $y=x$y=x, draw the inverse of $F\left(x\right)=2^x$F(x)=2x.
What sort of graph have you drawn?
Quadratic
Reciprocal
Logarithmic
Exponential
Hence state the equation of the logarithmic graph drawn.
Consider the function $f\left(x\right)=e^x$f(x)=ex.
The graph of $f\left(x\right)=\log x$f(x)=logx (grey) and $g\left(x\right)$g(x) (black) is drawn below.
The graph of $f\left(x\right)=\log x$f(x)=logx (grey) and $g\left(x\right)$g(x) (black) is drawn below.
$g\left(x\right)$g(x) is a transformation of $f\left(x\right)$f(x).