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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.

# Compound Problems

$$f(x) = \log_{60}(x^2)$$

What is the value of $$f(3)+f(4)+f(5)$$ ?

$\log_2(\sqrt{x}) + \log_4(x-3) = \log_{16}(9x^2)$

What value(s) of x satisfy this equation?

$2(\log_x(3)) + \log_3(x) = 3$

What is the sum of all real values of $$x$$ that satisfy the above equation?

$$f(x) = \log_{2}(x) - \log_{2^2}(x)$$ $$+ \log_{2^3}(x) - \log_{2^4}(x) \dots$$ $$+ \log_{2^{99}}(x) - \log_{2^{100}}(x)$$

What is the value of $$f(2^{(2^{100})}) - (2)f(2^{(2^{99})})$$ $$+ (2^2)f(2^{(2^{98})}) - (2^3)f(2^{(2^{97})}) \dots$$ $$+ (2^{98})f(2^{(2^{2})}) - (2^{99})f(2^{(2^{1})})$$ ?

Let $$f(x) = \log_{10}(\log_{10}(\log_{10}(x)))$$

The domain of $$f$$ is $$(k,\infty)$$

What is the value of $$k$$?

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