Question

If $x=lo{g}_5\left(1000\right)$ and $y=lo{g}_7\left(2058\right)$, then

• A. x>y
• B. x<y
• C. x=y
• D. None

Answer 1

The correct option is A x>y

$x=lo{g}_5\left(1000\right)=lo{g}_5\left(5^3.8\right)=3+lo{g}_{5}8>3+1=4$
$y=lo{g}_7\left(2058\right)=lo{g}_7\left(7^3.6\right)=3+lo{g}_{7}6>3+1=4$
since $x>4$ and $y<4$ $\therefore x>y$