# Express each of the following as a single logarithm: (1 / 2) log 36 + 2 log 8 - log 1.5.

The given logarithm is
$$1 / 2 \log 36+2 \log 8-\log 1.5=\log 36^{1 / 2}+\log 8^{2}-\log 1.5 \\ =\log (6)^{2 \times 1 / 2}+\log 8^{2}-\log (15 / 10) \\ =\log 6+\log 64-(\log 15-\log 10) \\ =\log (6 \times 64)-\log 15+\log 10 \\ =\log (6 \times 64 \times 10)-\log 15 \\ =\log [(6 \times 64 \times 10) / 15] \\ =\log (4 \times 64) \\ =\log 256$$