Use common logarithms or natural logarithms and a calculator

Use common logarithms or natural logarithms and a calculator to evaluate the expression. log_16 15 log_16 15 (Round to four decimal places.) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log_pi 68 log_pi 68 (Round the final answer to four decimal places as needed. Round all intermediate values to five decimal places as needed.) Use a graphing utility and the change-of-base property to graph the function. y = log_2 (x - 1) Each graph below uses a [- 1,10,1] by [- 6,6,1] viewing rectangle. Which graph is the correct graph of y = log_2 (x - 1)?

Solution

15 log₁₆15 = log(3*5) /log16 = [ log3 +log5]/(log2^4)

=[ log3 +log5]/4log2

plugging the values of lo3 , log5 , log2 from calculator

= 0.9767

16 log_pi68 = log68/log(pi)

use calculator to find value of log(pi) and log 68

So,  log68/log(pi) = 1.83251/0.49714 =3.6861

17. log₂(x-1) = log(x-1)/log2 = 3.32log(x-1)

x interecpt : 0 = log(x-1) ---> x= 2

(2, 0)

Option a and d pass through (2,0)

Out of these two a is correct because value of y = 3.32log(x-1) shall be

greater than log(x-1) and value at x=3 would be bigger so, graph would move away from x axis faster

So, option A