We have `log_(2)32 = 5` . Show that we get the same result by writing `32 = 2^(5)` and then using power rules. Verify the answer.

We know log_(2)32 = 5 . Show that we get the same answer by writing 32 as 64/2 and then using the product rule. Verify your answer .

We know that log_(10)100000 = 5 Show that you get the same answer by writing 100000 = 1000 xx 100 and then using the product rule. Verify the answer.

We can write log"" x/y = log (x.y^(-1 )) Can you prove that log"" x/y = log x - logy using product and power rules.

We know that, if 7 = 2^x then x = log_(2)7 . Then, what is the value of 2^(log_(2) 7 ) ? Justify your answer. Generalise the above by taking some more examples for a^(log_a N)

If sets A= (-3,2) and B= (-1, 5) then find the following sets :

Consider the points A(3,2,-4),B(5,4,-6) and C(9,8,-10) . i. Find AB, BC and AC and show that A, B, C are collinear. ii. Find the ratio in which B divides AC using distance formula. iii. Verify the result using section formula.

In case of a die is getting a 1 complementary to events getting 2, 3, 4, 5, 6? Give reasons for your answer

A fraction such that if the numerator is multiplied by 3 and the denominator is reduced by 3 we get ( 8)/( 11) but if the numerator is increased by 8 and the denominator is doubled we get (2) /( 5) .Find the fraction.

The sum of three numbers is 20. If we multiply the third number by 2 and add the first number to the result we get 23. By adding second and third numbers to 3 times the first number we get 46. Find the numbers using Cramer's rule.