Evaluating logarithms

Question

Assignment:

Q1. Sketch the graphs of y=5^x and y=-5^x+2-1 on the same set of axes. Identify the following properties of each graph:

a)the domains

b)the ranges

c)any asymptotes

d)the y-intercepts

Q2. The population of the U.S. doubles approximately every 100 years. In 1980 the population of the U.S. was 200 million. Find the projected population for the year 2180.

The formula for the population N(t) at any time t is

N(t)=C2^t/dwhere

C is the population at t=0

t is the time period elapsed

d is the doubling period of the population

Q3. Evaluate the following logarithms:

a)log₁₆2

b)log₇7

c)10^log10¹⁹

Q4. Solve the following equations:

a)log₈x=5

b)2^x-1=3

Provide complete and step by step solution for the question and show calculations and use formulas.