if log18 to the base 12=a and lod 54 to the base 24=b , then proove that ab + 5(a-b)=1.
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 AnswersTanishq 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
HENCE PROOVED
Provide a better Answer & Earn Cool Goodies
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Other Related Questions on algebra
Can we divide two vectors? If this is possible then how?
Can we divide two vectors? If this is possible then how?
algebra
1 Answer Available
Last Activity: 1 Year ago
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
1 Answer Available
Last Activity: 1 Year ago
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे
algebra
0 Answer Available
Last Activity: 2 Years ago