Question 1

If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$, then which of the following is/are true?

Accepted Answer

A)  $( f \circ g ) ( x ) = x$ and $( g \circ f ) ( x ) = x$ 
B)  $f$ is the inverse function of $g$ 
C)  $g$ is the inverse function of $f$ 
D)  All of the above are true.

Question 2

Scientists often use a process called carbon dating to estimate the age of archaeological finds. The process measures the amount of carbon-14, a radioactive isotope with a half-life of 5730 years. If a sample of wood from an ancient artifact had 13 grams of carbon-14 initially, the amount remaining, in grams, is given by $A ( t ) = 13 \left( \frac { 1 } { 2 } \right) ^ { t / 5730 }$ where t is the number of years since the tree died. How many grams would be present after 22,920 years?

Accepted Answer

The answer of Scientists often use a process called carbon...

Question 3

Evaluate without the use of a calculator. $\log _ { 6 } \frac { 1 } { 36 }$

Accepted Answer

A)  -2 
B)  4 
C)  12 
D)  2

Question 4

Solve the logarithmic equation. $$\log _ { 3 } x = 7$$

Accepted Answer

A)  $\left\{ 7 ^ { 3 } \right\}$ 
B)  $\left\{ 3 ^ { 7 } \right\}$ 
C)  $\{ 0.5646 \}$ 
D)  $\{ 1.7712 \}$

Exam 8: Exponential and Logarithmic Functions and Applications

If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$ , then which of the following is/are true?

Evaluate without the use of a calculator. $\log _ { 6 } \frac { 1 } { 36 }$

Solve the logarithmic equation. $\log _ { 3 } x = 7$

Exam 8: Exponential and Logarithmic Functions and Applications

If f(x) =x3−5f ( x ) = x ^ { 3 } - 5f(x) =x3−5 and g(x) =x+53g ( x ) = \sqrt [ 3 ] { x + 5 }g(x) =3x+5​ , then which of the following is/are true?

Evaluate without the use of a calculator. log⁡6136\log _ { 6 } \frac { 1 } { 36 }log6​361​

Solve the logarithmic equation. log⁡3x=7\log _ { 3 } x = 7log3​x=7

If $f ( x ) = x ^ { 3 } - 5$ and $g ( x ) = \sqrt [ 3 ] { x + 5 }$ , then which of the following is/are true?

Evaluate without the use of a calculator. $\log _ { 6 } \frac { 1 } { 36 }$

Solve the logarithmic equation. $\log _ { 3 } x = 7$