Algebra

Logarithmic Functions

Logarithm Problems

         

f(x)=log60(x2)f(x) = \log_{60}(x^2)

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

log2(x)+log4(x3)=log16(9x2)\log_2(\sqrt{x}) + \log_4(x-3) = \log_{16}(9x^2)

What value(s) of x satisfy this equation?

2(logx(3))+log3(x)=32(\log_x(3)) + \log_3(x) = 3

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

f(x)=log2(x)log22(x)f(x) = \log_{2}(x) - \log_{2^2}(x) +log23(x)log24(x)+ \log_{2^3}(x) - \log_{2^4}(x) \dots +log299(x)log2100(x)+ \log_{2^{99}}(x) - \log_{2^{100}}(x)

What is the value of f(2(2100))(2)f(2(299))f(2^{(2^{100})}) - (2)f(2^{(2^{99})}) +(22)f(2(298))(23)f(2(297))+ (2^2)f(2^{(2^{98})}) - (2^3)f(2^{(2^{97})}) \dots +(298)f(2(22))(299)f(2(21))+ (2^{98})f(2^{(2^{2})}) - (2^{99})f(2^{(2^{1})}) ?

Let f(x)=log10(log10(log10(x)))f(x) = \log_{10}(\log_{10}(\log_{10}(x)))

The domain of ff is (k,)(k,\infty)

What is the value of kk?

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