A logarithmic function, h, is plotted on the graph. What is the approximate rate of change of this function on the interval ?

answer: 590

step-by-step explanation:

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

to find d, you want to get all the numbers with the same denominator. since 210 is the largest number, and it can't be reduced, we want to set all the other denominators to 210.

our first number, 1/2, needs to be multiplied by 105 to get the denominator to be 210. the fraction will then be multiplied by 105/105 to get 105/210.

next, we want to get 1/6 to have a denominator of 210. 210/6 is 35, so we want to multiply 1/6 by 35/35 to get 35/210.

after that, we want to get 1/12 to have a denominator of 210. 12 goes into 210 17.5 times. we multiply 1/12 by 17.5/17.5 to get 17.5/210.

lastly, we 1/20 to have a denominator of 210 by mutiplying it by 10.5. 10.5/10.5 times 1/20 equals 10.5/210.

lastly we need to add all our converted numbers.

105/210 + 35/210 + 17.5/210 + 10.5/210 + 1/210 = 169/210