Math, asked by DevrajBose, 11 months ago

Find The Value Of :-
log base 7 √7√7√7.....

Answers

Answered by anmol3421

hope it helps if any problem....you may ask

Attachments:

DevrajBose: But The 3rd Step Is Confusing Me... Please Can You Describe It To Me?

anmol3421: in second step i got 1/2 which i multiplied to x

anmol3421: and x becomes 2x

anmol3421: next i used the property of log

anmol3421: log(ab) = log(a) + log(b)

Answered by aquialaska

Answer:

value of $log_7\,\sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}\:\:is\:\:1$

Step-by-step explanation:

Given: $log_7\,\sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}$

To find: It's value

We use the following results,

$log\,x^n=n\,log\,x\:\:and\:\:log\,mn=log\,n+log\,n$

let $x=log_7\,\sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}$

$x=log_7\,({7\sqrt{7\sqrt{7\sqrt{7...}}}})^{\frac{1}{2}}$

$x=\frac{1}{2}\times log_7\,7\sqrt{7\sqrt{7\sqrt{7\sqrt{7}...}}}$

$x=\frac{1}{2}\times(log_7\,7+log_7\,\sqrt{7\sqrt{7\sqrt{7\sqrt{7}...}}})$

$2x=log_7\,7+x$

$2x-x=log_7\,7$

$x=1$

Therefore, value of $log_7\,\sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}\:\:is\:\:1$

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