Prove that `(log)_7 10` is greater than `(log)_(11)13.`

Prove that log_7 11 is greater than log_(8)5 .

Prove log_(b) 1=0

Comprehension 2 In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8\ a n d(log)_(1/2)4 is larger than (log)_(1/2)8. Identify the correct order: (log)_3 8 (log)_3 8 > log_3 6 (log)_2 6 > log_3 6 (log)_4 6 < log_3 6

Prove log_(b)b = 1

Comprehension 2: In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8 and (log)_(1/2)4 is larger than (log)_(1/2)8 and (log)_(2/3)5/6 is- a. less than zero b. greater than zero and less than one c. greater than one d. none of these

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

Prove log_3(5) is irrational.

Prove log_(x)b^(x)=x

Prove the identity; (log)_a N* (log)_b N+(log)_b N * (log)_c N+(log)_c N * (log)_a N=((log)_a N*(log)_b N*(log)_c N)/((log)_(a b c)N)

Solve the following equaions for x and y log_(10)x+(1)/(2)log_(10)x+(1)/(4)log_(10)x+"...."=y " and " (1+3+5+"...."+(2y-1))/(4+7+10+"...."+(3y-1))=(20)/(7log_(10)x) .