Let N =103 log 2-2 log ( log 103)+ log (( log 106)2) where base of the logarithm is 10. The characteristic of the logarithm of N to the base 3 , is equal to

Question

Let N =103 log 2-2 log ( log 103)+ log (( log 106)2) where base of the logarithm is 10. The characteristic of the logarithm of N to the base 3 , is equal to (A) 2 (B) 3 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

N=10 P ; p = log 10 8- log 10 9+2 log 10 6 p = log ((8 ⋅ 36/9))= log 10 32 ∴ N =10 log 10 32=32 Hence characteristic of log 3 32 is 3 .

Q. Let $N = 1 0^{3 l o g 2 - 2 l o g (l o g 1 0^{3}) + l o g ((l o g 1 0^{6})^{2})}$ where base of the logarithm is 10. The characteristic of the logarithm of $N$ to the base 3 , is equal to

2

3

4

5

$N = 1 0^{P}; p = lo g_{10} 8 - lo g_{10} 9 + 2 lo g_{10} 6$
$p = lo g (\frac{8 \cdot 36}{9}) = lo g_{10} 32$
$∴ N = 1 0^{l o g_{10} 32} = 32$
Hence characteristic of $lo g_{3} 32$ is 3 .

Q. Let N=103log2−2log(log103)+log((log106)2) where base of the logarithm is 10. The characteristic of the logarithm of N to the base 3 , is equal to

2

3

4

5

N=10P;p=log10​8−log10​9+2log10​6 p=log(98⋅36​)=log10​32 ∴N=10log10​32=32 Hence characteristic of log3​32 is 3 .

Q. Let $N = 1 0^{3 l o g 2 - 2 l o g (l o g 1 0^{3}) + l o g ((l o g 1 0^{6})^{2})}$ where base of the logarithm is 10. The characteristic of the logarithm of $N$ to the base 3 , is equal to

$N = 1 0^{P}; p = lo g_{10} 8 - lo g_{10} 9 + 2 lo g_{10} 6$
$p = lo g (\frac{8 \cdot 36}{9}) = lo g_{10} 32$
$∴ N = 1 0^{l o g_{10} 32} = 32$
Hence characteristic of $lo g_{3} 32$ is 3 .