Finding logarithm by change-of-base formula

Question

Assignment:

Q1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered pairs to plot the graph of each function; please show graphs.

y = 2^x, x = 2^y

Q2. Solve the problem.

A rare baseball card was sold in 1990 for $285,000. The card was then resold in 1998 for $459,000. Assume that the card's value increases exponentially, and find an exponential function V(t) that fits the data. (Round decimals to three places.)

V(t) = 285e^0.766t, where t is the number of years after 1990.

V(t) = 285e^0.06t, where t is the number of years after 1990.

V(t) = 285,000e^0.766t, where t is the number of years after 1990.

V(t) = 285,000e^0.06t, where t is the number of years after 1990.

Q3. Solve the problem.

log_s 1/125 = x

Q4. Solve for x. Round to the nearest ten-thousandth.

log (225x²) = 3.456

Q5. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.

ln (x - 5) + ln (x + 4) = ln 36

Q6. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.

9^{(x - 2)} = 29

Q7. Find the logarithm using the change-of-base formula. Round to the nearest ten-thousandth.

log_π 14.2

Q8. Evaluate the exponential function for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; show or draw the graph. State the domain and the range of the function.

f(x) = e^x

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