Question

If (1.7)m=(0.17)n=100 then find the value of 1bym-1byn

Answer 1

M=1000/17

N=10000/17

1/m=17/1000

1/n=17/10000

1/m-1/n=17/1000-17/10000

=153/10000

Answer 2

$Given \: (1.7)m = (0.17)n= 100$

$i ) (1.7)m = 100$

$\implies 10 \times 1.7m= 10 \times 100$

$\implies 17m= 1000$

$\implies 17 = \frac{1000}{m}\\\implies \frac{17}{1000} = \frac{1}{m} \: --(1)$

$i ) (0.17)n= 100$

$\implies 100 \times 0.17n= 100 \times 100$

$\implies 17 = \frac{10000}{n}\\\implies \frac{17}{10000} = \frac{1}{n} --(2)$

$Now , \red{\frac{1}{m} - \frac{1}{n} }\\= \frac{17}{1000} - \frac{17}{10000} \\= 17\Big( \frac{1}{1000} - \frac{1}{10000} \Big)\\= 17\Big( \frac{10-1}{10000}\Big) \\= \frac{ 17 \times 9}{10000} \\= \frac{153 }{10000} \\= 0.0153$

Therefore.,

$\red{Value \: of \:\frac{1}{m} - \frac{1}{n} }\green {= 0.0153 }$

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