Algebra

# Logarithm 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 $k$?

×