Problems from Logarithms: definition and properties

Calculate the following logarithms:

$$log_5 25, \ log_3 \dfrac{1}{81}, \ log_{10}0,001$$ and $$log_9 3$$

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The resolution is based on trying to express the value of the number as a power of the base of the logarithm:

$$log_5 25= log_5 5^2=2$$

$$log_3 \dfrac{1}{81}=log_3 \dfrac{1}{3^4}=log_3 3^{-4}=-4$$


$$log_9 3=log_9 \sqrt{9}=log_9 9^{\frac{1}{2}}=\dfrac{1}{2}=0,5$$


$$2, -4, -3, 0,5$$

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