# Algebra - Week 6.2 - Logarithmics, Graphs, Word Problems

See the attached file.

1. 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 ...

2. 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.)

3. Solve the problem ...

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

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

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

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

8. 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 ...

(Please see attachment).

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#### Solution Preview

The solution file is attached.

1. 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 = 2x, x = 2y

(a) y = 2^x

x f(x) = 2^x

-3 0.1250

-2 0.2500

-1 0.5000

0 1.0000

1 2.0000

2 4.0000

3 8.0000

(b) x = 2^y

ln x = y ln 2

y = ln 2 x

x y = log 2 ...

#### Solution Summary

Complete, neat and step-by-step solutions for the logarithmics, graphs and word problems are provided in the attached file.