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Chapter 5: Q. 10 (page 351)

Use a calculator to evaluate each expression.
Round your answer to three decimal places.
$\log_{3} 21$

Short Answer

Expert verified

The value of $\log_{3} 21$ is 2.771

Step by step solution

01

Step 1. Given Information

Given Expression $\log_{3} 21$

We have to evaluate expression by using a calculator.

02

Step 2. Solution

For easier calculation on the calculator the base should be b = e

( i.e. we should have the natural logarithm )

Therefore, we will use the change of base formula:

$\log_{a} M = \frac{\log_{b} M}{\log_{b} a}$

In our case $\log_{a} M = \frac{\log_{e} M}{\log_{r} a} = \frac{\ln M}{I n a} - - - (1)$

So we have $\log_{3} 21 = \frac{\ln 21}{\ln 3} = 2.771$

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Most popular questions from this chapter

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ shown in the figure.

(a) $(g \circ f) (- 1)$ (b) $(g \circ f) (0)$ (c) $(f \circ g) (- 1)$ (d) $(f \circ g) (4)$ .

Vehicle Stopping Distance Taking into account reaction time, the distance $d$ (in feet) that a car requires to come to a complete stop while traveling $r$ miles per hour is given by the function

localid="1646198784356" $d (r) = 6.97 r - 90.39$

a. Express the speed $r$ at which the car is traveling as a function of the distance localid="1646198792401" $d$ required to come to a complete stop

b. Verify that localid="1646198797631" $r = r (d)$ is the inverse of localid="1646198802104" $d = d (r)$ by showing that localid="1646198806352" $r (d (r)) = r$ and localid="1646198811055" $d (r (d)) = d$

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" $300$ feet.

$d (r (d)) = d$

Solve the equation ${(\frac{1}{5})}^{x} = \frac{1}{25}$

and verify your results using a graphing utility.

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = 2 - e^{- x / 2}$

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = e^{x} - 1$

See all solutions

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