Grade 9Algebra

Please solve both questions....its related to logarithms

Question image for Please solve both questions....its related to log

Prakash Kumar

10 Years agoGrade 9

1 Answer

Ajay

Approved Tutor Answer10 Years ago

The attachment was not really clear, it took me lot of effort to understand the problem. From next time please post clear attachments.

Here are solutions to both problems

$Question\quad 1\quad \\ Given\quad { x }^{ 2 }\quad +\quad y^{ 2 }\quad =\quad 25xy\\ \quad { (x+y) }^{ 2 }\quad =\quad { x }^{ 2 }\quad +\quad y^{ 2 }\quad +\quad 2xy\quad =\quad 27xy\\ \quad taking\quad log\quad both\quad sides\\ \quad 2log(x+y)\quad =\quad log{ 3 }^{ 3 }xy\quad \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\quad 3log3\quad +\quad logx\quad +\quad logy\quad \\ \quad Hence\quad proved\\ \\ Question2:\\ Given\quad { x }^{ 2 }\quad +\quad y^{ 2 }\quad =\quad { z }^{ 2 }\\ { z }^{ 2 }\quad -\quad x^{ 2 }\quad =\quad { y }^{ 2 }\\ (z-x)(z+x)\quad =\quad { y }^{ 2 }\\ taking\quad log\\ Log(z+x)\quad +\quad Log(z-x)\quad =\quad 2Logy\\ \frac { Log(z+x) }{ Logy } \quad +\quad \frac { Log(z-x) }{ Logy } \quad \quad =\quad 2\\ { Log }_{ y }(z+x)\quad \quad +\quad { Log }_{ y }(z-x)\quad \quad =\quad 2\\ Hence\quad Proved\\ \\ \\$