Bounding ζ(s) in the critical strip

Assuming the Riemann Hypothesis, we make use of the recently discovered (Carneiro et al. (preprint) [1]) extremal majorants and minorants of prescribed exponential type for the function log(4+x2(α−1/2)2+x2) to find upper and lower bounds with explicit constants for log|ζ(α+it)| in the critical strip, extending the work of Chandee and Soundararajan (in press) [4].