Reliance Jio Logarithms Quiz 1

Answer: m + n = 1

Explanation: Simplify LHS, log \frac{m}{n} + log \frac{n}{m} = log \frac{m}{n} + \frac{n}{m} = 1,
So ,
=> log (m + n) = log 1
=> m + n = 1

log_{m} 36 + \frac{1}{2}log_{m} 256 - 2log_{m} 48
log_{m} 36 +log_{m} 256^{\frac{1}{2}} - log_{m} 48^{2}
log_{m} 36 + log_{m}16 -log_{m} 2304
log_{m}\frac{(36*16)}{2304}
log_{m}(\frac{1}{4})
-log_{m}4

Answer: 3

log_{2} 5 + log_{2} 1.6
log_{2}(5*1.6)
log_{2} 8
log_{2} 2 ^{3}
3log_{2} 2

3*1=3

Answer: 2y, 3+2y

Explanation: 1.
log_{2} m^{2}
2log_{2}m
2y

Answer: x=1/4log_{10}(1/4z)

Explanation:

z=4*10^{2x}
\frac{z}{4}=10^{22}
log_{b}(\frac{z}{4}) = log_{10}10^{2x}[/latex]
log_{10}(\frac{1}{4} z) = 2xlog_{10}10
x=\frac{1}{2}log_{10}(\frac{1}{4} z)

Answer: x= \frac{log y - log m} {log n}

Explanation: y=mn^{2}
=> log y = log(mn^2)
=> log y = log m+ log n^{2}
=> log y = log m+x log n
=> x log n=log y-log m
=> x= \frac{log y - log m} {log n}

Answer: x=5, x \not\equiv -5

Explanation:
2log_{10} + log_{10}3 = log_{10}75
log_{10}x^{2}+log_{10}3=log_{10}75
log(3x^{2})=log_{10}75
3a^{2}=75
x^{2}=25

Answer: x=5, x \not\equiv -2

Explanation :
=>log_{x}x+log_{a}(x-3)=log_{a}10
=>log_{a}[x(x-3)]=log_{a}10
=>x(x-3)=10
=>x^{2}-3a-10=0
=>(x-5)(x+2)=0
=>x=5 , x \not\equiv -2

Answer: l+2m , /fact{1}{2}-m

Explanation: i)
=> log_{a}100 = log_{a}(25*4)
=> log_{a}25+log_{a}4
=> log_{a}5^{2}+log_{a}4
=> 2log_{a}5+log_{a}4
=>2m+l
ii)
=> log_{a}(0.4) = log_{a} (\frac{2}{5})
=> log_{a}2-log_{a}5
=> log_{a}4^{\frac{1}{2}}-log_{a}5
=>\frac{1}{2} log_{a}4-log_{a}5
=>\frac{1}{2}l-m

Answer: t= \frac{1}{3}

Explanation:
=> log_{5}(4t+7)-log_{5}t=2
=>log_{5}\frac{(4t+7)}{t}=2log_{5}5
=>log_{5}\frac{(4t+7)}{t}=log_{5}25
=>\frac{4t+7}{t}=25
=>4t+7=25t
=>7=21t
=>t=\frac{1}{3}