Question

Help fast, ​please

Answer 1

ANSWER

1.

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

2.

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

3.

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

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,

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