The sum of all the values of a satisfying the equation `|[log_10 a,-1],[log_10(a-1),2]|=log_10 a+log_10 2`

The sum of all the values of a satisfying the equation `|[log_10 a,-1]

1.	The sum of all the values of a satisfying the equation `\|[log_10 a,-1],[log_10(a-1),2]\|=log_10 a+log_10 2`
Answer» Correct Answer - C `2log_(10)a+log_(10)(a-1)=log_(10)2a` `therefore a^(2)(a-1)=2a` `therefore a^(2)-a-2=0` `rArr (a-2)(a+1)=0` `rArr a=2,-1` (not possible) `therefore a = 2`

If `a gt 1, x gt 0` and `2^(log_(a)(2x))=5^(log_(a)(5x))`, then x is equal toA. `(1)/(10)`B. `(1)/(5)`C. `(1)/(2)`D. 1
If `x_(1)` and `x_(2)` are solution of the equation `log_(5)(log_(64)|x|+(25)^(x)-(1)/(2))=2x`, thenA. `x_(1)=2x_(2)`B. `x_(1)+x_(2)=0`C. `x_(1)=3x_(2)`D. `x_(1)x_(2)=64`
The value of x satisfying `5^logx-3^(logx-1)=3^(logx+1)-5^(logx - 1)` , where the base of logarithm is 10 is not : 67 divisible by
`log_(3/4)log_8(x^2+7)+log_(1/2)log_(1/4)(x^2+7)^(-1)=-2`.
Solve:`log_axlog_a(xyz)=48`;`log_aylog_a(xyz)=12`;`log_azlog_a(xyz)=84`
Solve : `root(4)(|x-3|^(x+1))=root(3)(|x-3|^(x-2))`.
Which of the following is/are true ?A. number of digits in `8^(12)5^(35)` is 35B. number of digits in `8^(12)5^(35)` is 36C. number of zeroes after decimal before a significant figures starts in `((8)/(27))^(20)` is 10D. number of zeroes after decimal before a significant figure starts in `((8)/(27))^(20)` is 11
If `log_(3)x-(log_(3)x)^(2)le(3)/(2)log_((1//2sqrt(2)))4`, then x can belong toA. `(-oo,1//3)`B. `(9,oo)`C. (1,6)D. `(-oo,0)`
The number of integers satisfying `log_((1)/(x))((2(x-2))/((x+1)(x-5)))ge 1` is
The value of `6^(log_10 40)*5^(log_10 36)` isA. 200B. 216C. 432D. none of these