Prove that, `log (1/2) +log (2/3) +log(3/4) +log(4/5) - log(1/5)=0`

Prove that log(1+2+3)=log1+log2+log3

int_0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a) log(2/3) (b) log(3/2) (c) log(3/4) (d) log(4/3)

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

Prove that log_3log_2log_(sqrt3) 81=1

Solve for x : (i) log_(10) (x - 10) = 1 (ii) log (x^(2) - 21) = 2 (iii) log(x - 2) + log(x + 2) = log 5 (iv) log(x + 5) + log(x - 5) = 4 log 2 + 2 log 3

If 0ltxlt1 , prove that: log(1+x)+log(1+x^2)+log(1+x^4)+… oo=-log(1-x)

Prove that: 2log(1+2+4+7+14)= log1+log2+log4+log7+log14

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

Solve for x: a) log_(x)2. log_(2x)2 = log_(4x)2 b) 5^(logx)+5x^(log5)=3(a gt 0), where base of log is 3.

Which of the following when simplified reduces to an integer? a. (2log6)/(log12+log3) b. (log32)/(log4) c. ((log)_5 15-(log)_5 4)/((log)_5 128) d. (log)_(1//4)(1/(16))^2