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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