Question

if (2.3) x=(0.23) y=1000 then find the value of x

Answer 1

2.3x=1000
⇒x=$\frac{1000}{2.3}= \frac{10000}{23} = 43 \frac{11}{23}$
Ans:x=$43 \frac{11}{23}$.
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Note:In this question , we need not find the value of y.

Answer 2

(2.3)^x=1000 and (0.23)^y=1000

log(2.3)^x =log1000 and log(0.23)^y=1000

xlog(2.3)=log10^3 and log(0.23)^y =log10^3

xlog(2.3) = 3log10 and ylog(0.23) =3log10

xlog(2.3) = 3×1 and ylog(0.23)=3  [log10=1]

⇒log(2.3)=3/x and log0.23 =3/y

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3/x -3/y =log2.3  -log(0.23)

3(1/x - 1/y) =log(2.3/0.23)

⇒1/x - 1/y ={log(10)}/3

⇒1/x-1/y =(1)/3

⇒1/x -1/y =1/3