Exercise

If $x = {\log }_{2}3, y = {\log }_{2}5$ then express ${\log }_{2}15$ in terms of $x$ and $y$.

Check whether the equations $2x + 3y = 1, 3x - y = 7$ have a unique solution, infinitely many solutions or no solution.

Find the points on the $y$-axis which is equidistant from the points $\mathrm{A}\left(6, 5\right)$ and $\mathrm{B}\left(- 4, 3\right)$.

For what positive value of $\text{'}p\text{'}$the following pair of linear equations have infinitely many solutions.

$px+3y-(p - 3)=0$

$12x+py-p=0$

Subba Rao started work in $1995$ at an monthly salary of $₹5000$ and received an increment of $₹200$ each year. In which year did his income reach $₹7000 ?$

Prove that$(\sqrt{2}+ \sqrt{3})$ is irrational.

$200$logs are stacked in the following manner :$20$logs in the bottom row, $19$ in the next row, $18$ in the row next to it and so on. In how many rows are the $200$ logs placed and how many logs are in the top row?

Draw a pair of tangents to a circle of radius $5 cm$which are inclined to each other at an angle of $60º.$