Simplify the following:
1) \(\log _9\left(\log _{27}\left(\log _{0.25}\left(\Large\frac{1}{64}\right)\right)\right)\)
2) \(\log _{\large{\frac{1}{\sqrt{2}}}}32\)
3) \(\log _4\left(-16\right)\)
4) \(\log_{0.1}\left(\Large\frac{1}{100}^{\Large\log_{\frac{2}{5}}\left(\frac{625}{16}\right)}\right)\)
5) \(\ln \left(\log _8\left(8^{\large{e^4}}\right)\right)\)
6) \(7^{\large\log _7\left(343\right)}\)
7) \(3\log_416-\log_3\frac{1}{3}+7\log_{100}10\)
Solution Bank
1) \(\log _9\left(\log _{27}\left(\log _{0.25}\left(\Large\frac{1}{64}\right)\right)\right)\)
2) \(\log _{\large{\frac{1}{\sqrt{2}}}}32\)
3) \(\log _4\left(-16\right)\)
4) \(\log_{0.1}\left(\Large\frac{1}{100}^{\Large\log_{\frac{2}{5}}\left(\frac{625}{16}\right)}\right)\)
5) \(\ln \left(\log _8\left(8^{\large{e^4}}\right)\right)\)
6) \(7^{\large\log _7\left(343\right)}\)
7) \(3\log_416-\log_3\frac{1}{3}+7\log_{100}10\)
Solution Bank