Exam 4: Exponential Functions, Logarithms, and E

Find the smallest integer M such that .

Evaluate assuming that log₃x = 12.3 and log₃y = 7.9.

Find a number x such that 10^2x + 10^x = 30. Round your answer to four decimal places.

Find all numbers x that satisfy the given equation. ln(x + 6) - ln(x - 6) = 5

Estimate the indicated value without using a calculator.

Suppose a colony of bacteria has a continuous growth rate of 20% per hour. By what percent will the colony have grown after 2 hours? Round your answer to the nearest tenth.

The full moon has an apparent magnitude of approximately -12.6. What would be the apparent magnitude of a star that was 14 times brighter than the full moon?

Suppose that you deposit into a savings account one dime on January 1, two dimes on January 2, four dines on January 3, and so on, doubling the amount of your deposit each day. After how many days, will your daily deposit exceed $100,000,000?

Evaluate the indicated expression. log ₃ 27

Evaluate Assuming that .

Find an integer k such that 19^k has 308 digits.

Estimate the indicated value without using a calculator.

Suppose that a colony of bacteria has a continuous growth rate of 28% per hour. If the colony contains 10,000 cells now, how many did it contain 8 hours ago?

Every function f with exponential growth can be represented by a formula of the form $f(x) = c2^{kx}$ for appropriate choices of c and k.

Estimate the value of . Give the answer as a power of e.

Find a formula for (f g)(x) assuming that .

Suppose x is such that . Evaluate . Round your answer to three decimal places.

Estimate the value of . Give the answer as a power of e.

Evaluate assuming that .

is $2^{13,746} < 13,746^{1000}$ correct?