__Example 4__Given that ${\mathrm{log}}_{2}3=1.585$ and ${\mathrm{log}}_{2}5=2.322$ , evaluate the following.

(a) ${\mathrm{log}}_{8}15$

(b) ${\mathrm{log}}_{5}0.6$

(c) ${\mathrm{log}}_{15}30$

(d) ${\mathrm{log}}_{16}45$

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