Exam 14: Exponential and Logarithmic Functions

Write the logarithmic statement in exponential form. log ₁₀1,000,000 = 6

Given that log 2 5 = 2.3219 and log 2 7 = 2.8074, evaluate the expression $\log _ { 2 } \sqrt [ 8 ] { 5 }$ by using properties: For positive real numbers b , r and s , where b $F$ 1, and for any real number p , $\log b r s = \log b r + \log b s$ $\log b \frac { r } { s } = \log b r - \log b s$ $\log b r ^ { p } = p \left( \log _ { b } r \right)$

Solve the logarithmic equation. $\log ( x + 8 ) - \log ( 2 x + 1 ) = \log x$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log 9.16$

Use your calculator to find x when given ln x . $\ln x = - 1.8336$ Please round the answer to the nearest hundredth.

Find f - -1 ( x ). f ( x ) = x $-$ 3

Use the formula $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the amount for the investments. $2,200 for 5 years at 1.5% compounded annually. Please round the answer to the nearest hundredth. $A =$ $__________ $2,200 for 5 years at 1% compounded quarterly. Please round the answer to the nearest hundredth. $A =$ $__________ Determine which investment amounts to more. __________

All graphs of $f ( x ) = b ^ { - x }$ contain the point $( 1,0 )$ .

Use your calculator to find x when given ln x . $\ln x = 5.3876$ Please round the answer to the nearest hundredth.

For a certain strain of bacteria, the number of bacteria present after t hours is given by the equation Q = Q _oe^{0.34 t} where Q _o represents the initial number of bacteria. How long will it take 400 bacteria to increase to 4,000 bacteria? Express answer to the nearest tenth.

The base for common logarithms is 10.

Form the inverse function f ^{- -1}, and list the domain and range of f ^{- -1}. f = {(0, 0), (2, 6), (-1, -1), (-2, -6)} Match the name of each set in the left column with the corresponding set in the right column. - $\{ ( 0,0 ) , ( 6,2 ) , ( - 1 , - 1 ) , ( - 6 , - 2 ) \}$

Graph the exponential function. $f ( x ) = \left( \frac { 8 } { 7 } \right) ^ { x }$

Use the formulas $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ or $A = p \mathrm { e } ^ { r t }$ to find the amount for the investment. $10,800 for 5 years at 5% compounded continuously.

Assuming that the rate of inflation is 4% per year, the equation P = P _o (1.04) ^t yields the predicted price P , in t years, of an item that presently costs P _o. Find the predicted price of a $0.95 soft drink in 9 years. The choices are rounded to the nearest cent.

Solve the equation. $\left( \frac { 1 } { 6 } \right) ^ { x } = \frac { 1 } { 36 }$

Solve the equation. $3 ^ { x } = 27$

Write $2 ^ { - 4 } = \frac { 1 } { 16 }$ in logarithmic form.

Evaluate the expression. $5 ^ { \log 52 }$

Given that log 8 5 = 0.7740 and log 8 11 = 1.1531, evaluate the expression $\log _ { 8 } \sqrt [ 7 ] { 11 }$ by using properties: For positive real numbers b , r and s , where b $\neq$ 1, and for any real number p , $\log b r s = \log _ { b } r + \log _ { b } s$ $\log b \frac { r } { s } = \log{ b }^ r - \log b^ s$ $\log _ { b } r ^ { p } = p \left( \log _ { b } r \right)$ Please give the answer to four decimal places.