Exponentials & Logarithms

Problem requiring decisions

Problem

Some equations involving powers or indices can be solved using logarithms… but not all.

Think about how you could go about solving the following equations. Sort them according to the tools or methods you would use.

$3^x=81$

$x^5=50$

$3^x=43$

$5^{2x}-5^x-6=0$

$5^x+4^x=8$

$5^x+2\times5^{1-x}=7$

$3^{2x}-3=24$

$2^{2x}-9\times2^x+8=0$

$\sqrt{2x-3}=5$

$5^x-x^5=3$

$16^{\frac{3}{x}}=8$

$\left(\dfrac{13}{16}\right)^{3x}=\dfrac{3}{4}$

You might find it helpful to have the equations printed on cards that you can rearrange as you sort them.

Can you write some other equations to go in each of your sorting categories?