if log18 to the base 12=a and lod 54 to the base 24=b , then proove that ab + 5(a-b)=1.
Sourav Dash , 7 Years ago
Grade 12th pass
Algebra> if log18 to the base 12=a and lod 54 to t...
1 Answers
Tanishq Chourishi
Last Activity: 7 Years ago
here a=log1218 =log3*49*2= (2log3 +log2)/(log3+2log2) because logxy=(logy)/(logx)
simmillarly b= log2454=(log(27*2))/(log(8*3))=(3log3+log2)/(log3+3log2)
now let us assume log3=x
and log2=y
then a=( 2x+y)/(x+2y) and b= (3x+y)/(x+3y)
now a*b=(2x+y)(3x+y)/(x+2y)(x+3y)
= (6x2 +5xy+y2) /(x2+5xy+6y2)
and 5(a-b)=5(-x2+y2)/(x2 +5x*y +6y2) take lcm and simplify u are expected to get the resultant as shown beside …..
now ab+5(a-b) =(x2+5xy+6y2)/(x2+5xy+6y2)
=1
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