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Chapter 5: Q 78. (page 309)

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places.
$\log_{π} \sqrt{2}$

Short Answer

Expert verified

$0.303$

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{π} \sqrt{2}$

02

Step 2. Calculation.

Apply the base change formula and simplify.

$\begin{array}{l} \log_{π} \sqrt{2} = \frac{\log \sqrt{2}}{\log π} \\ = \frac{1}{2} (\frac{\log 2}{\log π}) \\ = \frac{0.605}{2} \\ \approx 0.303 \end{array}$

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Most popular questions from this chapter

If $f (x) = a^{x}$ , show that $\frac{f (x + h) - f (x)}{h} = a^{x} . \frac{a^{h} - 1}{h} h \neq 0$ .

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{3 x + 4}{2 x - 3}$

Use the graph of $y = f (x)$ given in Problem $44$ to evaluate

the following:

(a) $f (2)$

(b) $f (1)$

(c) $f^{- 1} (0)$

(d) $f^{- 1} (- 1)$

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

solve each equation

$9^{2 x} 27^{x^{2}} = 3^{- 1}$

See all solutions

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