Prove that : `"2 log" (15)/(18) - "log" (25)/(162) + "log" (4)/(9) = log 2`

Simplify : 2 log ""( 15)/(8) - log ""( 25)/( 162) +3 log ""( 4)/(9)

Express in terms of log 2 and log 3 : (i) log 36 (ii) log 144 (iii) log 4.5 (iv) "log"(26)/(51) - "log" (91)/(119) (v) "log"(75)/(16) - "2 log" (5)/(9) + "log" (32)/(243)

prove that log2 + 16 log(16/15) + 12 log(25/24) + 7 log(81/80) = 1

Prove that : (i) (log a)^(2) - (log b)^(2) = log((a)/(b)).log(ab) (ii) If a log b + b log a - 1 = 0, then b^(a).a^(b) = 10

Find the value of 7 log(16/15) + 5 log (25/24) + 3 log (81/80) .

Simplify : log""(75)/( 16) - 2 log ""( 5)/(9) +log""( 32)/(243)

Prove that : (log_(2)10)(log_(2)80)-(log_(2)5)(log_(2)160)=4 .

If "log"_(3) x + "log"_(9)x^(2) + "log"_(27)x^(3) = 9 , then x =

Prove that log_2log_2log_(2) 16 =1

Statement-1: The solution set of the equation "log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x) 2 "is" {2^(-sqrt(2)), 2^(sqrt(2))}. Statement-2 : "log"_(b)a = (1)/("log"_(a)b) " and log"_(a) xy = "log"_(a) x + "log"_(a)y