Logarithms

Hong Kong

Stage 4 - Stage 5

Consider the function $F\left(x\right)=2^x$`F`(`x`)=2`x`.

a

Graph the function.

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b

Add the line $y=x$`y`=`x` to the graph.

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c

By reflecting points on the curve $F\left(x\right)=2^x$`F`(`x`)=2`x` over the line $y=x$`y`=`x`, draw the inverse of $F\left(x\right)=2^x$`F`(`x`)=2`x`.

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d

What sort of graph have you drawn?

Quadratic

A

Reciprocal

B

Logarithmic

C

Exponential

D

e

Hence state the equation of the logarithmic graph drawn.

Easy

Approx 5 minutes

Consider the function $f\left(x\right)=\left(\frac{1}{5}\right)^x$`f`(`x`)=(15)`x`.

Consider the function $f\left(x\right)=e^x$`f`(`x`)=`e``x`.

Consider the function $f\left(x\right)=5\times2^x$`f`(`x`)=5×2`x` shown in the graph.

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