Chapter 6 Test

Determine whether the function $$f\left(x\right)=\left(\frac{1}{3}\right)^x$$ represents exponential growth, decay, or neither. (a)  

Determine whether the function $$y\ =\ 5^x$$ represents exponential growth, decay, or neither.​ (a)  

Simplify the expression.

$$\frac{20e^3}{10e^6}$$

Simplify the expression.

$$\left(-3e^{-5x}\right)^2$$

Evaluate the logarithm.

$$\log_28$$

Describe the transformation of f represented by g.

$$f\left(x\right)=\log_4x;\ \ g\left(x\right)=4\log_4x-3$$

Expand or condense the logarithmic expression.

$$\log_83xy$$

Solve the equation.

Round your answer to two decimal places.

$$2e^{6x}-\ 16\ =\ 4$$

Solve the equation.

$$8^{3x}=8^{12}$$

Write an exponential function $$y\ =\ ab^x$$ represented by the graph above.