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.

Find 32 ^((2)/( 5))

Show that the points A (4, 2), B (7, 5) and C (9, 7) are three points lying on a same line.

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)

Consider a closed loop C in a magnetic field as shown in figure. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula phi=vecB_1 . dvecA_1 + vecB_2 . dvecA_2 +…. Now if we choose two different surfaces S_1 and S_2 having C as their edge, would we get the same answer for flux. Justify your answer.

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

Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) By using product rule

Figure Show plot of PV//T versus P for 1.00xx10^(-3) kg of oxygen gas at two different temperatures. (a) What does the dotted plot signify? (b) Which is true: T_(1) gt T_(2) or T_(1) lt T_(2) ? (c) What is the value of PV//T where the curves meet on the y-axis? (d) If we obtained similar plots for 1.00xx10^(-3) kg of hydrogen, would we get the same value of PV//T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV//T (for low pressure high temperature region of the plot) ? (Molecular mass of H_(2) = 2.02 u, of O_(2) = 32.0 u, R= 8.31Jmol^(-1)K^(-1).)