`log_10⁡ (k^2/l^2) + log_10⁡ (l^2/m^2) + log_10⁡ (m^2/k^2) = ?`

[log_10⁡(x)]^2 − log_10⁡(x^3) + 2=0

log_10⁡ a + log_10 ⁡b = log_10⁡ (a+b)

log4^2_10 + log4_10

If log_(10)m=(1)/(2) , then log_(10)10m^(2)=

The derivative of (log)_(10)x w.r.t. x^2 is equal to 1/(2x^2)log_e 10 (b) 2/(x^2)(log)_(10)e 1/(2x^2)(log)_(10)e (d) none of these

Find x, if : (i) log_(10) (x + 5) = 1 (ii) log_(10) (x + 1) + log_(10) (x - 1) = log_(10) 11 + 2 log_(10) 3

Given log_(10 ) x = 2a and log_(10) y = (b)/(2) . If log_(10) P = 3a - 2b express P in terms of x and y.

Given system of simultaneous equations 2^x\ . 5^y=1\ a n d\ 5^(x+1). 2^y=2. Then - (a) . x=(log)_(10)5\ a n d\ y=(log)_(10)2 (b) . x=(log)_(10)2\ a n d\ y=(log)_(10)5 (c) . x=(log)_(10)(1/5)\ a n d\ y=(log)_(10)2 (d) . x=(log)_(10)5\ a n d\ y=(log)_(10)(1/2)

For the system of equation "log"_(10) (x^(3)-x^(2)) = "log"_(5)y^(2) "log"_(10)(y^(3)-y^(2)) = "log"_(5) z^(2) "log"_(10)(z^(3)-z^(2)) = "log"_(5)x^(2) Which of the following is/are true?

Evaluate each of the following without using tables : (i) log 5 + log 8 - 2 log 2 (ii) log_(10) 8 + log_(10) 25 + 2 log_(10)3 - log_(10) 18 (iii) log 4 + (1)/(3) log 125 - (1)/(5) log 32