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Chapter 5: Q 12. (page 308)

True or False $\frac{\ln 8}{\ln 4} = 2$

Short Answer

Expert verified

False

Step by step solution

01

Step 1. Given Information.

Consider the given information.

$\frac{\ln 8}{\ln 4} = 2$

02

Step 2. Calculation.

Consider the left side of the given equation and simplify.

$\begin{array}{rcl} \frac{\ln 8}{\ln 4} & = & \frac{\log 2^{3}}{\log 2^{2}} \\ = & \frac{3 \log 2}{2 \log 2} \\ = & \frac{3}{2} \end{array}$

03

Step 3. Conclusion.

Since the left side is not equal to the right side.
The given statement is false.

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Most popular questions from this chapter

As the base a of an exponential function $f (x) = a^{x}$ , where $a > 1$ increases, what happens to the behavior of its graph for $x > o ?$ What happens to the behavior of its graph for $x < 0 ?$

If $5^{- x} = 3$ , what does $5^{3 x}$ equal?

The graphs of $y = a^{- x}$ and $y = {[\frac{1}{a}]}^{x}$ are identical. Why?

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

and verify your results using a graphing utility.

Height and Head Circumference. The head circumference

C of a child is related to the height H of the child (both in inches) through the function $H (C) = 2.15 C - 10.53$

(a) Express the head circumference C as a function of height H.

(b) Verify that $C = C (H)$ is the inverse of $H = H (C)$ by showing that $H (C (H)) = H$ and $C (H (C)) = C$ .

(c) Predict the head circumference of a child who is $26$ inches tall.

See all solutions

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