Mathematics: Fast, a. expand the following and state the law that is indicated. 1. log4(3x) 2. log3(27/x) 3. log4(x5)

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Fast, a. expand the following and state the law that

Ответ:

bobiscool3698

17.01.2022

Mathematics

ANSWER

$log_{4}(3x) = log_{4}(3) + log_{4}(x)$

$log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)$

$log_{4}( {x}^{5} ) = 5 log_{4}(x)$

EXPLANATION

1. The given logarithmic expression is

$log_{4}(3x)$

Use the product rule:

$log_{a}(mn) = log_{a}(m) + log_{a}(n)$

We apply this rule to obtain:

$log_{4}(3x) = log_{4}(3) + log_{4}(x)$

2. The given logarithmic expression is

$log_{3}( \frac{27}{x} )$

We apply the quotient rule:

$log_{a}( \frac{m}{n} ) = log_{a}(m) - log_{a}(n)$

This implies that;

$log_{3}( \frac{27}{x} ) = log_{3}(27) - log_{3}(x)$

We simplify to get;

$log_{3}( \frac{27}{x} ) = log_{3}( {3}^{3} ) - log_{3}(x)$

Apply the power rule:

$log_{a}( {m}^{n} ) = n log_{a}(m)$

$log_{3}( \frac{27}{x} ) = 3 log_{3}( {3}) - log_{3}(x)$

simplify;

$log_{3}( \frac{27}{x} ) = 3 (1) - log_{3}(x)$

$log_{3}( \frac{27}{x} ) = 3 - log_{3}(x)$

3. The given logarithmic expression is;

$log_{4}( {x}^{5} )$

Apply the power rule of logarithms.

$log_{a}( {m}^{n} ) = n log_{a}(m)$

This implies that,

$log_{4}( {x}^{5} ) = 5 log_{4}(x) .$

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Fast,

a. expand the following and state the law that is indicated.

1. log4(3x)

2. log3(27/x)

3. log4(x5)

Ответ:

Ответ:

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