To Log or Not to Log?
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.
| $3^x=81$ | $x^5=50$ | $3^x=43$ | $5^{2x}-5^x-6=0$ |
| $5^x+4^x=8$ | $5^x+2\times5^{1-x}=7$ | $3^{2x}-3=24$ | $2^{2x}-9\times2^x+8=0$ |
| $\sqrt{2x-3}=5$ | $5^x-x^5=3$ | $16^{\frac{3}{x}}=8$ | $\big(\frac{13}{16}\big)^{3x}=\frac{3}{4}$ |
You might find it helpful to have the equations printed on cards that you can rearrange as you sort them. They are available here: cards.pdf
Can you write some other equations to go in each of your sorting categories?
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.
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