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 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 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.

Charles Richter defined the magnitude of an earthquake to be M = log_(10) (I/S) , where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicentre of the earthquake) and S is the intensity of a ''standed earthquake'' (whose amplitude is 1 micron =10^(-1) cm). Each number increase on the Richter scale indicates an intensity ten times stronger. For example. an earthquake of magnitude 5. An earthquake of magnitude 7 is 100 times stronger then an earthquake of magnitude 5. An earthquake of magnitude 8 is 1000 times stronger than an earthquake of magnitude 5. The earthquake in city A registered 8.3 on the Richter scale. In the same year, another earthquake was recorded in city B that was four times stronger. What was the magnitude of the earthquake in city B ?

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.

In has been estimated that the total energy radiated by the sun is 3.8xx10^26 J per second. The source of energy of stars is a thermonuclear reaction called nuclear fusion. Fusion reactions are not controlled. It is presumed that the energy of stars is due to two processes called proton-proton cycle and carbon nitrogen cycle. Fusion cannot take place at ordinary temperature. This, hydrogen bomb uses a small fission bomb, which on explosion causes the temperature to rise very high about 10^7 K. We have yet to see how a hydrogen bomb can be used for peaceful life-sustaining purpose. Energy released in the process of fusion is due to mass defect. It is also called Q-value. Q =Deltamc^2 , Deltam= mass defect Answer the following questions based on above passage: Fusion reaction takes place at about:

Asha's uncle was advised by his doctor to have an MRI(magnetic resonance imaging) scan of his brain. Her uncle felt that it was too expensive and wanted to postpone it. When Asha learnt about this, she took the help of her family and when she approached the doctor, he also offered a substantial discount. She thus convinced her uncle to undergo the rest to enable the doctor to know the condition of his brain. the reusling information greatly helped his doctor to treat him properly. Based on the above paragraph, answer the following questions. Assuming thet MRI was perpformed using a magnetic field of 0.1T . find teh maximum and minimum values of the force that the magnetic field could exert on a proton (Charge =1.6xx10^(-19)C) that was moving with a speed of 10^(4)m//s .