Question

if (6.2)^x=(0.62)^y =1000 then find the value of 1/x-1/y
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100 points​

Answer 1

Answer:

♧ ᴀɴsᴡᴇʀ♧

Hence value of 1/x - 1/y = 1/1000

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Answer 2

${\large\orange{\mathbb\fcolorbox{yellow}{maroon}{■ \: Solution:-}}}$

$6.2 {}^{x} = (0.62) {}^{y} = 1000 \\ 6.2 { }^{x} = 1000 \\ x \: log(6.2) = 1000 \\ \sf \implies \: x = \frac{1000}{ log(6.2) } - - (1) \\ \\ (0.62) {}^{y} = 1000 \\ y \: log(0.62) = 1000 \\ \implies \sf \: y = \frac{1000}{ log(0.62) } - - (2)$

☆ According to question :-

• Find the value of $\frac{1}{x} - \frac{1}{y}$

$\boxed{\frac{1}{x} - \frac{1}{y} } \\ \\ \implies \frac{ log \: 6.2 }{1000} - \frac{ log \: 0.62 }{1000 } \\ \\ \implies \frac{ log \: 62 \: - log \: 0.62}{1000} \\ \\ \implies \frac{log \frac{6.2}{0.62} }{1000} \\ \\ \implies \frac{log \: 10}{100} \\ \\ we \: know \: log10 = 1\\ \\ : \implies \boxed{ \sf \green{ \frac{1}{100} } }$

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@Mahor2111

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