Question

(4.7)^x = (0.047) ^y = 1000 then find the value of 1/x- 1/y

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

Given :

${(4.7)}^{x} = {(0.047)}^{y} = 1000$

We take the 1st and 3rd term.

Then, we apply (log) :

${(4.7)}^{x} = 1000 \\ \\ = > \: log ({4.7})^{x} = log \: (1000) \\ \\ = > log \: {(4.7)}^{x} = log \: ({10})^{3} \\ \\ = > x \: log(4.7) = 3 \: log(10) \\ \\ = > x = \frac{3}{log(4.7)} \: \: since \: \: log \: (10) = 1$

Again, we take the 2nd and 3rd term.

Then, we apply (log) :

${(0.047)}^{y} = 1000 \\ \\ = > log \: {(0.047)}^{y} = log \: {(10)}^{3} \\ \\ = > y \: log(0.047) = 3 \: log(10) \\ \\ = > y = \frac{3}{log(0.047)}$

Now,

$\frac{1}{x} = \frac{log(4.7)}{3} \\ \\ and \\ \\ \frac{1}{y} = \frac{log(0.047)}{3}$

Now,

$\frac{1}{x} - \frac{1}{y} \\ \\ = \frac{log(4.7)}{3} - \frac{log(0.047)}{3} \\ \\ = \frac{1}{3} ( \: log(4.7) - log(0.047)) \\ \\ = \frac{1}{3}( log \frac{4.7}{0.047} ) \\ \\ = \frac{1}{3} \: log(100) \\ \\ = \frac{1}{3} \: log( {10})^{2} \\ \\ = \frac{1}{3} \times 2 \times log(10) \\ \\ = \frac{2}{3}$

Remember :

log (a/b) = log a - log b

log (ab) = log a + log b

log (a^n) = n log a

♧♧HOPE THIS HELPS YOU♧♧

Answer 2

HELLO DEAR,

i think something is mistake in your questions

right questions is like that;-

(4.7)^x = (0.047) ^y = 10000 then find the value of 1/x- 1/y

Read more on Brainly.in - https://brainly.in/question/2770513

given that:-

(0.47)^x =(0.0047)^y =10000

-----------------condition--(1)------------------

(0.47)^x = 10000

=> (0.47)^x =100²

=> (0.47) = 100^(2/x)-------------(1)

------------------condition--(2)--------------------

(0.0047)^y=10000

=> (0.47/100)^y=100²

=> (0.47)^y = 100^(2+y)

=> (0.47) = 100^(2+y)/y-----------(2)

-------from --(1) and---(2)

we get,

100^(2+y)/y = 100^(2/x)

(2+y)/y = 2/x

=> 2/y +1 = 2/x

=>
$\frac{2}{x} - \frac{2}{y} = 1 \\ \\ = > 2( \frac{1}{x} - \frac{1}{y} ) = 1 \\ \\ = > \frac{1}{x} - \frac{1}{y} = \frac{1}{2}$

I HOPE ITS HELP YOU DEAR,
THANKS