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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 468 (page 1068)

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.
$5 \log_{4} x + 3 \log_{4} y$

Short Answer

Expert verified

The value is $\log_{4} x^{5} y^{3}$

Step by step solution

01

Step 1. Given

An expression is given as $5 \log_{4} x + 3 \log_{4} y$

02

Step 2. Calculation

Use property $\log_{a} M^{p} = p \log_{a} M$ ,

$5 \log_{4} x + 3 \log_{4} y = \log_{4} x^{5} + \log_{4} y^{3}$

Now use property $\log_{a} M + \log_{a} N = \log_{a} M N$

$5 \log_{4} x + 3 \log_{4} y = \log_{4} x^{5} y^{3}$

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Most popular questions from this chapter

In the following exercises, graph, on the same coordinate system, the inverse of the one-to-one function shown.

In the following exercise, find the inverse of each function.

$x^{3} - 4$

In the following exercises, solve each equation.

$4^{x + 2} = 64$

In the following exercises, find

a. $f \circ g (x)$

b. $g \circ f (x)$

c. $(f . g) (x)$

For functions $f (x) = 4 x - 3$ and

$g (x) = 6 x - 5$ , find

$(f \circ g) (x)$
$(g \circ f) (x)$
$(f \cdot g) (x)$

See all solutions

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