Question

log(√5√5√5........infinity) to the base 5

Answer 1

$heya \\ \\ \\ formulla \: of \: log \\ \\ \\ 1) \\ log(mnpq...) = log(m) + log(n) + log(p) + log(q) + ... \\ \\ \\ \\ 2) \: \: log(x {}^{1 \div n} ) = 1 \div n log(x) \\ \\ \\ 3) \: \: \: log_{z}(z) = 1 \\ \\ \\ \\ log_{5}( \sqrt{5} \times \sqrt{5} \times \sqrt{5} \times ...) \\ \\ log_{5}( \sqrt{5} ) + log_{5}( \sqrt{5} ) + log_{5}( \sqrt{5} ) + ... \infty \\ \\ log_{5}(5 {}^{1 \div 2} ) + log_{5}5 {}^{1 \div 2} ) + log_{5}(5 {}^{1 + 2} ) + ... \infty \\ \\ 1 \div 2(1 + 1 + 1 + ... \infty )$