Exercise 2 (Rewriting Before Differentiating). (2a) Use the properties of logarithms to reurite the expression f(2) = In (x°/=² +1) (2b) Now use (a) to find f'(x)

A culture of bacteria undergoes exponential growth according to the equation below, where t is given in hours, and the bacteria are measured in thousands y = 150 (3)¹ a) How much bacteria is present after 2 hours? b) When will there be 300 bacteria? Express your answer in terms of logarithms.

Now consider a logarithmic function g(x)=log(x) Is it true that log(10+100)=log(10)+log(100)? Is it true that log(a+b)=log a + log b ? Explain your reasoning.

Loga(U2V2)