Question

का मान ज्ञात कीजिए।
यदि 3^a = 27^b = 81^c और abc = 144 है, तो 12 (1/a+1/2b+1/5c)=?​

Answer 1

Answer:

${3}^{a} = {27}^{b} = {81}^{c}$

${3}^{a} = {3}^{3b} = {3}^{4c}$

$so \: \: a = 3b = 4c$

now,

$abc = 144$

$4c \times \frac{4c}{3} \times c = 144$

${c}^{3} = \frac{144 \times 3}{4 \times 4} = 9 \times 3 = 27$

$c = 3 \: \: \: so \: a = 12 \: and \: b = \frac{4 \times 3}{3} = 4$

so ,

$12 \times ( \frac{1}{a} + \frac{1}{2b} + \frac{1}{5c} ) = 12 \times ( \frac{1}{12} + \frac{1}{8} + \frac{1}{15} ) = 12 \times \frac{10 + 15 + 8}{120} = 12 \times \frac{33}{120} = \frac{33}{10}$