Question

0.23^x=0.023^y=1000 find 1/x-1/y

Answer 1

i kept a pic
hope this helps u

Answer 2

Answer: $\frac{1}{3}$

Step-by-step explanation:

Here,

$0.23^x=1000$  ( Given )

By taking log on both side,

$xlog(0.23)=log(1000)$

$\frac{log(0.23)}{log(1000)}=\frac{1}{x}$

Now,

$0.023^y=1000$

Taking log on both sides,

$ylog(0.023)=log(1000)$

$\frac{log(0.023)}{log(1000)}=\frac{1}{y}$

Hence,

$\frac{1}{x}-\frac{1}{y}=\frac{log(0.23)}{log(1000)}-\frac{log(0.023)}{log(1000)}$

$=\frac{log(0.23)}{log(10^3)}-\frac{log(0.023)}{log(10^3)}$

$=\frac{log(0.23)}{3log10}-\frac{0.023}{3log10}$   ( $loga^b=bloga$ )

$=\frac{log(0.23)}{3}-\frac{log(0.023)}{3}$ ( log 10 = 1 )

$=\frac{1}{3}[log(0.23)-log(0.023)]$

$=\frac{1}{3}\times log(\frac{0.23}{0.023})$ ( log a - log b = log(a/b) )

$=\frac{1}{3}\times log(10)$

$=\frac{1}{3}$