Question

If 2^a =3^b =7^c =42 then calculate 1/a+1/b+1/c?​

Answer 1

Answer:

sorry I didn't get answer.

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ {2}^{a} = {3}^{b} = {7}^{c} = 42 }$

TO DETERMINE

The value of

$\displaystyle \sf{ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} }$

EVALUATION

Here it is given that

$\displaystyle \sf{ {2}^{a} = {3}^{b} = {7}^{c} = 42 }$

Thus we get

$\displaystyle \sf{ 2 = {42}^{ \frac{1}{a} } }$

$\displaystyle \sf{ 3= {42}^{ \frac{1}{b} } }$

$\displaystyle \sf{ 7= {42}^{ \frac{1}{c} } }$

Now

$\displaystyle \sf{ 2 \times 3 \times 7 = 42}$

$\displaystyle \sf{ \implies \: {42}^{ \frac{1}{a} } \times {42}^{ \frac{1}{b} } \times {42}^{ \frac{1}{c} } = 42}$

$\displaystyle \sf{ \implies \: {42}^{ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} } = 42}$

$\displaystyle \sf{ \implies \: {42}^{ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} } = {42}^{1} }$

$\displaystyle \sf{ \implies \: \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1}$

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