Exam 12: Logarithmic and Exponential Functions

Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { x } ( 3 y z )$

Solve. -Use the formula N = Iekt, where N is the number of items at time t, I is the initial amount, and k is a growth constant equal to the percent of growth (expressed in decimal form) per unit of time. There are currently 70 million cars in a certain country, increasing by 3% annually. How many Years will it take for this country to have 97 million cars? Round to the nearest year.

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _ { 7.4 } 5.0$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = \left( \frac { 1 } { 5 } \right) ^ { x } - 2$ A) Horizontal asymptote: $y = - 2$ ; Domain: $( - \infty , \infty )$ , Range: $( - 2 , \infty )$ B) Horizontal asymptote: $\mathrm { y } = \frac { 1 } { 5 }$ ; Domain: $( - \infty , \infty )$ , Range: $\left( \frac { 1 } { 5 } , \infty \right)$ C) Horizontal asymptote: $y = 2$ ; Domain: $( - \infty , \infty )$ , Range: $( 2 , \infty )$ D) Horizontal asymptote: $\mathrm { y } = 0$ ; Domain: $( - \infty , \infty )$ , Range: $( 0 , \infty )$

Expand. Assume that all variables represent positive real numbers. - $\log _ { 5 } \left( \frac { x ^ { 5 } y ^ { 6 } } { 4 } \right)$

Evaluate. Round to the nearest thousandth, if necessary. - $\log 0.0586$

Rewrite using the power and product rules. Assume all variables represent positive real numbers. - $\log _ { 6 } \sqrt { 2 x }$

Rewrite using the power and product rules. Assume all variables represent positive real numbers. - $\ln x ^ { 4 } y ^ { 5 } z ^ { 2 }$

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _ { 9 } 0.888$

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 6 } 6 + \log _ { 6 } 8$

Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent positive real numbers. - $\log _ { 4 } ( 10 x )$

Evaluate the given function. - $f ( x ) = 4 ^ { x } + 2 , \quad f ( 2 )$

Evaluate the given function. -f(x) = 12log3 (x - 3), f(12)

Evaluate using the change-of-base formula. Round to four decimal places. - $\log _ { 6 } 0.91$

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of this function. - $f ( x ) = 4 ^ { x + 2 } - 2$

Rewrite using the power and product rules. Assume all variables represent positive real numbers. - $\log _ { \mathrm { b } } \mathrm { yz } 8$

Suppose for some base b > 0 (b ≠ 1) that logb 2 = A, logb 3 = B, logb 5 = C, and logb 7 = D. Express the given logarithms in terms of A, B, C, or D. - $\log _ { b } \left( \frac { 1 } { 4 } \right)$

Solve. -Susan purchased a painting in the year 2000 for $3000. Assuming an exponential rate of inflation of 3.8% per year, how much will the painting be worth 7 years later?

Find all intercepts for the given function. Round to the nearest tenth if necessary. - $f ( x ) = 5 ( x + 1 ) - 1$

Simplify. - $10 ^ { \log _ { 10 } 3 }$