Without using your calculators (except to check your answers), determine or deduce the following logarithms. State the exponential relations which suggest or confirm your answers in each case.

(a) log₁₆8 (b) log_0.11000 (c) log₈32 (d) log₈16

Using only the information: log_b2 = 0.3445, log_b5 = 0.8000, and log_b7 = 0.9672 to four decimal places, compute each of the following logarithms. You may use the basic properties of logarithms here, but you may not use a built-in logarithmic function key on your calculator. Show your work. Do not attempt to determine the value of the base b first.

(a) log_b35 (b) log_b49 (c) logb3.5 (d) logb(105.12)