Exam 14: Exponential and Logarithmic Functions

Express $\log b \left( \frac { x ^ { \frac { 1 } { 2 } } y ^ { \frac { 1 } { 5 } } } { z ^ { 8 } } \right)$ as the sum or difference of simpler logarithmic quantities. Assume that all variables represent positive real numbers.

Use the formula $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the amount for the investment. $13,400 for 4 years at 1.5% compounded semiannually.

Perform the following calculations and express answer to the nearest hundredth. $\frac { \log 10 } { \log 4 }$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = 2.1434$

Solve the equation. $27 ^ { 38 x } = 9 ^ { x + 7 }$

Solve the equation. $10 ^ { x } = 0.1$

Perform the following calculations and express answer to the nearest hundredth. $\frac { \ln 5 } { 2 \ln 2 }$

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 investments. $10,500 for 5 years at 4% compounded continuously. Please round the answer to the nearest hundredth. $A =$ $__________ $10,500 for 5 years at 4.5% compounded quarterly. Please round the answer to the nearest hundredth. $A =$ $__________ Determine which investment amounts to more. __________

Solve the exponential equation 9 ^{x - 9} = 42 and express approximate solutions to the nearest hundredth.

Graph the exponential function. $f ( x ) = 4 ^ { x }$

Write 10 ⁵ = 100,000 in logarithmic form.

Graph the function $y = 2 + \log _ { 2 } x$ . Remember that the graph of $f ( x ) = \log _ { 2 } x$ is given.

Given that log 8 5 = 0.7740 and log 8 11 = 1.1531, evaluate the expression $\log _ { 8 } \left( \frac { 121 } { 5 } \right)$ by using properties: For positive real numbers b , r and s , where b $\neq$ 1, and for any real number p , $\log b r s = \log b r + \log b s$ $\log b \frac { r } { s } = \log b r - \log b s$ $\log b r ^ { p } = p ( \log b r )$

Solve the logarithmic equation. ln( 5 x + 3 ) = ln6 + ln ( x $-$ 1 )

Solve the equation. $\log _ { x } 5 = \frac { 1 } { 5 }$

True or false? The function below is one-to-one function. f ( x ) = $-$ x 8

To determine the amount of time for a principal to double, triple, etc. when compounded continuously at r % interest, use the formula $A = P e ^ { r t }$ .

Suppose it is estimated that the value of a car depreciates 30% per year for the first 10 years. The equation $A = P _ { 0 } ( 0.7 ) ^ { t }$ yields the value ( A ) of a car after t years if the original price is P o . Find the value (to the nearest dollar) of $16,000.00 car after 2 years.

Write the logarithmic statement in exponential form. $\log 3 \left( \frac { 1 } { 243 } \right) = - 5$

Approximate the logarithm log₃15 to three decimal places.