Question

If $lo{g}_{m^x}>lo{g}_{m^y}$ which of the following statements is / are true ?

1.$x>yifm>1$

2.$x<yifm>1$

3.$x>yif0<m<1$

4.$x<yif0<m<1$

• A. Only 1 and 3
• B. Only 2 and 3
• C. Only 1 and 4
• D. Only 2 and 4

Answer 1

The correct option is C

Only 1 and 4

It is given that $lo{g}_{m}x>lo{g}_{m}y$

Now, we can take the condition 1

When $m>1$

If $m>1.lo{g}_{m}x$ is an increasing function

Graph of $lo{g}_{m}xwhenm>1$

If $lo{g}_{m}x>lo{g}_{m}y$

$x>y$

so,statement 1 is correct and statement 2 is wrong.

Condition 2: when $0<m<1$

If $0<m<1.Lo{g}_{m}x$ is a decreasing function. If value of x increases $lo{g}_{m}x$

decreases.

Graph of $lo{g}_{m}xwhen0<m<1$

If $lo{g}_{m}x>lo{g}_{m}y$

$0<m<1$

So, $x<y$ statement 4 is correct and statement 3 is wrong.

Only statement 1 $\&$ 4 is correct.