Are your logs clear?

Algebra Level 5

How many statements are always true?

  • \(\log_{2} (x^{45}) = 45\log_{2} (x)\)

  • \(\log_{2} xy = \log_{2} x + \log_{2} y\)

  • \(\log_{3}x = \dfrac{1}{\log_{x}3}\)

  • \(\log_{3}8 = \dfrac{\log_{156}8}{\log_{156}3}\)


\(x\) is a real number not equal to \(0\).

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