Explicit bounds on the logarithmic derivative and the reciprocal of the Riemann zeta-function

The purpose of this article is consider |ζ′(σ +it)/ζ(σ + it)| and |ζ(σ +it)|^-1 when σ is close to unity. We prove that |ζ′(σ + it)/ζ(σ + it)| ≤ 87 log t and |ζ(σ + it)|^-1≤ 6.9 × 10⁶ log t for σ ≥ 1-1/(8 log t) and t ≥ 45.