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## Logarithmic Functions

Logarithmic scales are used when the range of possible values is very wide, such as the intensity of an earthquake or the acidity of a liquid, in order to avoid the use of large numbers.

# Level 1

$\large \log_7 35 + \log_7 35 - \log_7 25 = \ ?$

$\large\log_{\color{green}{y}}{\color{blue}{x}}+\log_{\color{blue}{x}}{\color{green}{y}}=-2$ Find the value of $$\color{blue}{x}\color{green}{y}.$$

If $$4 \log_{12} \left(x^9\right) + \log_{12} \left(x^6\right) = 126$$, find $$x.$$

$\frac{1}{\log_{2}{100!}}+\frac{1}{\log_{3}{100!}}+\frac{1}{\log_{4}{100!}}+\ldots+\frac{1}{\log_{100}{100!}}= \ ?$

Find the smallest number among the following numbers:

(A) $$\log_{2015}2016$$

(B) $$\log_{2016}2017$$

(C) $$\log_{2017}2018$$

(D) $$\log_{2018}2019$$

(E) $$\log_{2019}2020$$

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