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log 54 to the base 3/log 3 to the base 486-log 1458 to the base 3/log 3 to the base 18=x Find the value of x. Please give the solution

log 54 to the base 3/log 3 to the base 486-log 1458 to the base 3/log 3 to the base 18=x
Find the value of x.
Please give the solution

Grade:10

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
{log54 to the base 3/log3 to the base 486}-{log1458 to the base 3/log3 to the base 18=x
{log54 to the base3.log3 to the base 18-log1458 to the base3.log3 to the base486}/{log3 to the base 486.log3 to the base 18}=x
(log 54 to the base 18-log 1458 to the base 486)/(log3 to the base 486log 3 to the base18)=x
{log(18*3) to the base 18 -log(486*3) to the base 486}/{log3 to the base 486.log3 to the base 18}=x
{(log 18 to the base 18 +log 3 to gthe base 18)-(log486 to the base 486 +log 3 to the base 486)}/{log3 to the base 486.log 3 to the base 18}=x
(log 3 to the base 18 - log 3 to the base 486)/log3 to the base 486.log 3 to the base 18 =x
{(log3/log18)-(log3/log486)}/(log3/log486).(log3/log18) =x
(log 486 -log 18)/ log 3 =x
log (486/18)/log 3=x
log 27/log3 =x
3log3/log3=x
3=x

Ans is x=3

thanks & Regards
Rinkoo Gupta
AskIITians Faculty

Arpit Kumar
31 Points
7 years ago
A bit complicated and long but the correct method. Thanks

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