`[ [ loge , loge^2 , loge^3 ] , [ loge^2 , loge^3 , loge^4 ] ,[ loge^3 , loge^4 , loge^5 ]]`

int \ 1/x{loge^(e x)*loge^(e^2x) * loge^(e^3x)}dx

int \ 1/x{loge^(e x)*loge^(e^2x) * loge^(e^3x)}dx

Solve : log_e (x-a) + log_e x =1 (a>0)

Let a_1, a_2, a_3, ..., a_10, be in G.P. with a_i gt0 for i = 1, 2, ......., 10 and S be the set of pairs (r,k), r, k in NN (the set of natural numbers) for which |(log_e a_1^ra_2^k,log_e a_2^ra_3^k,log_e a_3^ra_4^k), (log_e a_4^ra_5^k,log_e a_5^ra_6^k,log_e a_6^ra_7^k), (log_e a_7^ra_8^k,log_e a_8^ra_9^k,log_e a_9^ra_10^k)|=0. Then the number of elements in S, is

Find the area bounded by y=log_e x , y=-log_e x ,y=log_e(-x),a n dy=-log_e(-x)dot

Find the area bounded by y=log_e x , y=-log_e x ,y=log_e(-x),a n dy=-log_e(-x)dot

I=int \ log_e (log_ex)/(x(log_e x))dx

I=int \ log_e (log_ex)/(x(log_e x))dx

Let bi gt 1 for i = 1, 2, ...., 101 . Suppose log_e b_1, log_e b_2, ...., log_e b_101 are in Arithmetic Progression (A.P.) with the common difference log_e 2 . Suppose a_1, a_2, ....., a_101 are in A.P. such that a_1 = b_1 and a_51 = b_51 . If t = b_1 + b_2 + .... + b_51 and s = a_1 + a_2 + .... + a_51 , then .