Express ln 1 = 0 in its equivalent exponential form.
Write the equation in exponential form:
ln 9 = 2.20
Express e3 20.09 in logarithmic form.
Write the equation in logarithmic form:
e4 = 54.6
Evaluate the natural logarithm without a calculator.
ln e5
Simplify and if the expression is undefined, say so:
Write as a single logarithm:
ln 3 + ln 7
3 ln 5 – ln 19
Rewrite the expression in condensed form:
2 ln x + ln y + ln 8
Expand the following expression:
ln 10x3
Rewrite the expression using natural logarithms. Then evaluate the expression to the thousands place.
Solve for x:
ex = 4
Solve the equation.
e3x + 2 = 40
ln x = 17
ln (x – 6) = –2
ln x2 = 24
ln (2x – 5) = 17
Simplify the equation by using the properties of logarithms. Then solve it. (Use the quadratic formula if necessary).
ln x – ln (x – 2) = 3
ln (y + 4) + ln (y – 2) = 5
e2x – 8ex + 15 = 0
Give the range and domain of the function:
f(x) = ln (x – 3)
f(x) = ln | x – 1|
Draw the graph of y = ln x. Check whether it meets x–axis at any point.
Sketch the graph of the function:
f(x) = –ln 2x
Determine the range and the domain of the function.
The number of DVD's sold in a year has been increasing exponentially.
A model is given by , where t is the number of years since 1990. Find the number of DVD's that would be sold in the year 2005, if it follows the same model.
The amount ( in billion dollars) spent on the defense services in a country is modeled by
A = 284.92 + 6.25t + 25.45 ln t,
where t is the number of years since 2002. About how much amount will be spent in 2006?
