Exponentials and Logarithms

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There are 12 main questions in this chapter. These can be broken down into dozens of simpler questions. You will be tested by all of them. This test may be quite long. We recommend doing this test on a computer or tablet, not on a smartphone.

Do not guess any answers, you would only cheating yourself. If you think you know the answer from memory but cannot explain why it is the answer, then select the "I don't know" option. You are here to get an honest assessment of your progress, for your own benefit.

These questions cover the curriculum for this topic. This test will let you know how strong you are on this topic, if you treat it properly. Bluffing and guessing are counter-productive to your goal.

1. Re-write the following as a single logarithm \(\frac{log_{g}{f}}{log_{g}{y}}\)
2. What is \((s^{b})^{c}\) ?
3. What is \(n^{0}\) ?
4. What is equivalent to \((q \times k)^{g}\) ?
5. What is \(\frac{m^{h}}{m^{u}}\) ?
6. What is \(p^{\frac{1}{q}}\) ?
7. Simplify the following exponential \(c^{log_{c}{r}}\)
8. What is equivalent to \(h^{-m}\) ?
9. What is \(log_{f}{o}-log_{f}{m}\) ?
10. What is \(log_{k}{(s^{q})}\) in terms of \(log_{k}{s}\)?
11. What is \(log_{2}{f}+log_{2}{y}\) ?
12. What is \(u^{p} \times u^{w}\) ?