Exam 4: Exponential and Logarithmic Functions

The graph of a logarithmic function is shown. Select the function which matches the graph. - A) $f ( x ) = - \log _ { 3 } x$ B) $f ( x ) = \log _ { 3 } x$ C) $f ( x ) = 1 - \log _ { 3 } x$ D) $f ( x ) = \log _ { 3 } ( - x )$

Find the domain of the composite function f $f ^ { \circ } g$ - $f ( x ) = \frac { 6 } { x + 1 } ; \quad g ( x ) = x + 2$

Solve the problem. -In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation $\mathrm { P } ( \mathrm { t } ) = \frac { 240 } { 5 + 54.99 \mathrm { e } ^ { - 0.0208 \mathrm { t } } }$ , where t is the number of years since 1990. Estimate the year when the population will be 21 million.

Solve the equation. - $3 ^ { 6 - 3 x } = \frac { 1 } { 27 }$

Find the exact value of the logarithmic expression. - $\log _ { 5 } \sqrt { 5 }$

Find functions f and g so that f $f \circ g = H$ - $\mathrm { H } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 1 }$

Solve the problem. Round your answer to three decimals. -What annual rate of interest is required to triple an investment in 7 years?

The graph of a logarithmic function is shown. Select the function which matches the graph. - A) $f ( x ) = - \log _ { 3 } x$ B) $f ( x ) = 1 - \log _ { 3 } x$ C) $f ( x ) = \log _ { 3 } ( - x )$ D) $f ( x ) = \log _ { 3 } x$

Solve the equation. - $\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4$

Solve the equation. - $\log _ { 2 } ( 3 x - 2 ) - \log _ { 2 } ( x - 5 ) = 4$

Find the present value. Round to the nearest cent. -To get $10,500 after7 years at 4% compounded annually

Solve the problem. - $\text { Find the value of } \log _ { 3 } 4 \cdot \log _ { 4 } 5 \cdot \log _ { 5 } 6 \cdot \log _ { 6 } 7 \cdot \log _ { 7 } 8 \cdot \log _ { 8 } 9$

Solve the problem. -The price $p$ of a certain product and the quantity sold $x$ obey the demand equation $p = - \frac { 2 } { 3 } x + 200,0 \leq x \leq 300$ . Suppose that the cost $C$ of producing $x$ units is $C = \frac { \sqrt { x } } { 20 } + 800$ . Assuming that all items produced are sold, find the cost $C$ as a function of the price $p$ .

Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round your answer to three decimal places. - $\log _ { 3.2 } 57$

Decide whether or not the functions are inverses of each other. - $f ( x ) = ( x - 2 ) ^ { 2 } , x \geq 2 ; g ( x ) = \sqrt { x } + 2$

Solve the equation. - $\log _ { 4 } ( x + 5 ) + \log _ { 4 } ( x - 1 ) = 2$

Solve the problem. - $\text { If } f ( x ) = x ^ { 2 } \text { and } g ( x ) = - 1 + 5 x \text {, find } ( f \circ g ) ( x ) \text { and find the domain of } ( f \circ g ) ( x )$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $4 ^ { x + 6 } = 7$

Solve the equation. - $\log _ { y } 14 = 2$

Choose the one alternative that best completes the statement or answers the question. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. - $3 ( 2 x - 1 ) = 19$