There are relatively prime positive integers m and n so that ( m / n )= log 4(32 log 9 27), then the value of (m+n) is equal to

Question

There are relatively prime positive integers m and n so that ( m / n )= log 4(32 log 9 27), then the value of (m+n) is equal to (A) 17 (B) 19 (C) 21 (D) 23

Tardigrade Admin · Accepted Answer

( m / n )= log 4(32 log 9 27)= log 4(32(3/2))= log 4(2(15/2))=(15/4)

Q. There are relatively prime positive integers $m$ and $n$ so that $\frac{m}{n} = lo g_{4} (3 2^{l o g_{9} 27})$ , then the value of $(m + n)$ is equal to

17

19

21

23

$\frac{m}{n} = lo g_{4} (3 2^{l o g_{9} 27}) = lo g_{4} (3 2^{\frac{3}{2}}) = lo g_{4} (2^{\frac{15}{2}}) = \frac{15}{4}$

Q. There are relatively prime positive integers m and n so that nm​=log4​(32log9​27), then the value of (m+n) is equal to

17

19

21

23

nm​=log4​(32log9​27)=log4​(3223​)=log4​(2215​)=415​

Q. There are relatively prime positive integers $m$ and $n$ so that $\frac{m}{n} = lo g_{4} (3 2^{l o g_{9} 27})$ , then the value of $(m + n)$ is equal to

$\frac{m}{n} = lo g_{4} (3 2^{l o g_{9} 27}) = lo g_{4} (3 2^{\frac{3}{2}}) = lo g_{4} (2^{\frac{15}{2}}) = \frac{15}{4}$