The value of 13log10125 - 2log104 + log1032 :

Correct Answer: 0

Explanation:

= log tan 1 0 + log tan 89 0 + log tan 2 0 + log tan 88 0 + ? ? + log tan 45 0  

 

= log [ tan 1 0 × tan 89 0 ] + log [ tan 2 0 × tan 88 0 ] + ? ? + log 1  

 

? tan ( 90 - ? ) = c o t ? a n d tan 45 0 = 1  

 

= log 1 + log 1 +.....+log 1 

 

= 0.

Correct Answer: 3/2

Explanation:

  $$\begin{gathered} = log 3 3 + log 2 3 + log 10 3 log 10 × 3 × 2 2 \\ \end{gathered}$$ 

 

 

 

= log 3 3 1 2 + log 2 3 + log 10 3 1 2 log ( 10 × 3 × 2 2 )  

 

 

 

 

 

 

 

= 1 2 log 3 3 + 3 log 2 + 1 2 log 10 3 log 10 + log 3 + log 2 2  

 

 

 

 

 

 

 

= 3 2 log 3 + 2 log 2 + log 10 log 3 + 2 log 2 + log 10 =  3 2  

Correct Answer: -5

Explanation:

log (0.0000134). Since there are four zeros between the decimal point and
the first significant digit, the characteristic is ?5.

Correct Answer: 3

Explanation:

log 10 5 + log 5 x + 1 = log 10 x + 5 + 1

log 10 5 5 x + 1 = log 10 10 x + 5

5 5 x + 1 = 10 x + 5

5x+1=2x+10

3x=9

x=3

 

 

Correct Answer: p > q

Explanation:

k l > k + 1 l + 1 for (k,l) > 0 and  k > l 

 

 

 

Let     k = x+1    and   l = x

 

 

 

Therefore,  x + 1 x > ( x + 1 ) + 1 ( x ) + 1

 

 

 

 (x + 1) > x

 

 

 

Therefore,  log ( x + 1 ) log ( x ) > log ( x + 2 ) log ( x + 1 )

 

 

 

? log x x + 1 > log x + 1 x + 2

Correct Answer: 2

Explanation:

Given  a 2 + b 2 = c 2

 

Now   1 log c + a b + 1 log c - a b

 

=  log b c + a + log b c - a

 

=  log b c 2 - a 2

=  2 log b b = 2

Correct Answer: 3(1-a-b)

Correct Answer: log (2 + 3) = log (2 x 3)

Explanation:

log (2 + 3) = log 5

 

log (2 x 3) = log 2 + log 3

 

 log (2 + 3) ?log (2 x 3)

Correct Answer: 0

Explanation:

By trial and error method, when we substitute 

x = 0

Both LHS and RHS are equal.

Correct Answer: 1