Intermediate Algebra 2e

# Practice Test

### Practice Test

447.

For the functions, $f(x)=6x+1f(x)=6x+1$ and $g(x)=8x−3,g(x)=8x−3,$ find $(f∘g)(x),(f∘g)(x),$ $(g∘f)(x),(g∘f)(x),$ and $(f·g)(x).(f·g)(x).$

448.

Determine if the following set of ordered pairs represents a function and if so, is the function one-to-one. ${(−2,2),(−1,−3),(0,1),(1,−2),(2,−3)}{(−2,2),(−1,−3),(0,1),(1,−2),(2,−3)}$

449.

Determine whether each graph is the graph of a function and if so, is it one-to-one.

450.

Graph, on the same coordinate system, the inverse of the one-to-one function shown.

451.

Find the inverse of the function $f(x)=x5−9.f(x)=x5−9.$

452.

Graph the function $g(x)=2x−3.g(x)=2x−3.$

453.

Solve the equation $22x−4=64.22x−4=64.$

454.

Solve the equation $ex2e4=e3x.ex2e4=e3x.$

455.

Megan invested $21,00021,000$ in a savings account. If the interest rate is $5%,5%,$ how much will be in the account in 8 years by each method of compounding?
compound quarterly
compound monthly
compound continuously.

456.

Convert the equation from exponential to logarithmic form: $10−2=1100.10−2=1100.$

457.

Convert the equation from logarithmic equation to exponential form: $3=log73433=log7343$

458.

Solve for x: $log5x=−3log5x=−3$

459.

Evaluate $log111.log111.$

460.

Evaluate $log4164.log4164.$

461.

Graph the function
$y=log3x.y=log3x.$

462.

Solve for x:
$log(x2−39)=1log(x2−39)=1$

463.

What is the decibel level of a small fan with intensity $10−810−8$ watts per square inch?

464.

Evaluate each. $6log6176log617$
$log99−3log99−3$

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible.

465.

$log 5 25 a b log 5 25 a b$

466.

$ln e 12 8 ln e 12 8$

467.

$log 2 5 x 3 16 y 2 z 7 4 log 2 5 x 3 16 y 2 z 7 4$

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.

468.

$5 log 4 x + 3 log 4 y 5 log 4 x + 3 log 4 y$

469.

$1 6 log x − 3 log ( x + 5 ) 1 6 log x − 3 log ( x + 5 )$

470.

Rounding to three decimal places, approximate $log473.log473.$

471.

Solve for x:
$log7(x+2)+log7(x−3)=log724log7(x+2)+log7(x−3)=log724$

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

472.

$( 1 5 ) x = 9 ( 1 5 ) x = 9$

473.

$5 e x − 4 = 40 5 e x − 4 = 40$

474.

Jacob invests \$14,000 in an account that compounds interest quarterly and earns $4%.4%.$ How long will it take for his money to double?

475.

Researchers recorded that a certain bacteria population grew from 500 to 700 in 5 hours. At this rate of growth, how many bacteria will there be in 20 hours?

476.

A certain beetle population can double in 3 months $(A=2A0).(A=2A0).$ How long will it take for that beetle population to triple?

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