If log 10 2= a , log 10 3= b then log 0.72(9.6) in terms of a and b is equal to

Question

If log 10 2= a , log 10 3= b then log 0.72(9.6) in terms of a and b is equal to (A) (2 a+3 b-1/5 a+b-2) (B) (5 a+b-1/3 a+2 b-2) (C) (3 a+b-2/2 a+3 b-1) (D) (2 a+5 b-2/3 a+b-1)

Tardigrade Admin · Accepted Answer

log 0.72(9.6)= log (72/100)((96/10))=(( log 10 96- log 10 10)/( log 10 72- log 10 100)) =( log 10(25 × 3)-1/ log 10(23 × 32)-2)=((5 a+b-1/3 a+2 b-2))

Q. If $lo g_{10} 2 = a, lo g_{10} 3 = b$ then $lo g_{0.72} (9.6)$ in terms of $a$ and $b$ is equal to

$\frac{2 a + 3 b - 1}{5 a + b - 2}$

$\frac{5 a + b - 1}{3 a + 2 b - 2}$

$\frac{3 a + b - 2}{2 a + 3 b - 1}$

$\frac{2 a + 5 b - 2}{3 a + b - 1}$

$lo g_{0.72} (9.6) = lo g_{\frac{72}{100}} (\frac{96}{10}) = \frac{( l o g _{10} 96 - l o g _{10} 10 )}{( l o g _{10} 72 - l o g _{10} 100 )}$
$= \frac{l o g _{10} ( 2 ^{5} \times 3 ) - 1}{l o g _{10} ( 2 ^{3} \times 3 ^{2} ) - 2} = (\frac{5 a + b - 1}{3 a + 2 b - 2})$

Q. If log10​2=a,log10​3=b then log0.72​(9.6) in terms of a and b is equal to

5a+b−22a+3b−1​

3a+2b−25a+b−1​

2a+3b−13a+b−2​

3a+b−12a+5b−2​