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Question Number 137764 by byaw last updated on 06/Apr/21

$$\mathrm{If}{\log }_{2}3=a\mathrm{and}{\log }_{3}7=b,\mathrm{express}$$$${\log }_{42}56\mathrm{in}\mathrm{terms}\mathrm{of}a\mathrm{and}b$$

Answered by EnterUsername last updated on 06/Apr/21

$${log}_{2}3=a,{log}_{3}7=\frac{{log}_{2}7}{{log}_{2}3}=b\Rightarrow {log}_{2}7=ab$$$${log}_{42}56=\frac{{log}_{2}56}{{log}_{2}42}=\frac{{log}_2\left(8\times 7\right)}{{log}_2\left(6\times 7\right)}=\frac{{log}_2{2}^3+{log}_{2}7}{{log}_{2}2+{log}_{2}3+{log}_{2}7}$$$$=\frac{3+ab}{1+a+ab}$$

Commented by otchereabdullai@gmail.com last updated on 08/Apr/21

$$\mathrm{wow}!$$

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