Question

could you kindly help me with exercise 9K all questions ?

expression on each side of the equation the argument of a Make the expressie carithm with baseb. los al = log, yog, a = log, log, logx bringing the power down on the left-hand side) (dividing both sides by log,a ) Therefore, log. x e when a, b, x > 0. log x= where a, b, x>0. log, Example 13 Functions Find the value of log, 20 to 3 significant figures by converting to a base 10. b base e. Comment on your answers to parts a and b. a log, 20 = 108 20 = 2.73 log 3 Using log.x - log log, blog, 20 20 In 20 in 20 = 2.73 In 3 Changing to base 10 or base e still gives the same value for log, 20. You can use the "change of base formula" to change a logarithm to an expression which involves logarithmic terms in any base you choose. Example 14 If log, 7 = p and log, 9 = 4. find log, in terms of pand 4. log, 9 log2_4 Using log x box and changing to base 4 log, 7 P Exercise OK 4 Prove that logy -logo loge 1 Find the value of each of these expressions. a log, 8 b log, 24 clog, 8 dlog, 30 a log, 1 / + log, 2 If p = log, A and q = log, B, find log, Bin terms of p and q. If log 3-r and log 6 = s, write each of these expressions in terms of rands • log,6 b log 3 clog, 36 d log, 54 e log 6 flog 18 g log, 2 5 Show that In 10 6 Explain the difference between the word "prove" and "show that in the last two questions. 412

Answer 1

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