5.08 Equations with exponentials and logarithms

Interactive practice questions

The graphs of $y=3^x$y=3x (labelled $B$B) and $y=x$y=x (labelled $A$A) have been plotted below.

By reflecting $y=3^x$y=3x about the line $y=x$y=x, plot the graph of the inverse of $y=3^x$y=3x.

Easy
Less than a minute

The graphs of $y=3^{-x}$y=3x (labelled $B$B) and $y=x$y=x (labelled $A$A) have been plotted below.

By reflecting $y=3^{-x}$y=3x about the line $y=x$y=x, plot the graph of the inverse of $y=3^{-x}$y=3x.

The graphs of $y=\left(\frac{1}{2}\right)^x$y=(12)x (labelled $B$B) and $y=x$y=x (labelled $A$A) have been plotted below.

By reflecting $y=\left(\frac{1}{2}\right)^x$y=(12)x about the line $y=x$y=x, plot the graph of the inverse of $y=\left(\frac{1}{2}\right)^x$y=(12)x.

The graphs of $y=\log_2x$y=log2x (labelled $B$B) and $y=x$y=x (labelled $A$A) have been plotted below.

By reflecting $y=\log_2x$y=log2x about the line $y=x$y=x, plot the graph of the inverse of $y=\log_2x$y=log2x.

Outcomes

VCMNA360 (10a)

Solve simple exponential equations.