What is expand log_{9}(\sqrt[7]{(s^6t)/(81)}) ?

The solution to expand log_{9}(\sqrt[7]{(s^6t)/(81)}) is -2/7+(log_{9}(t))/7+(6log_{9}(s))/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{9}(\sqrt[7]{(s^6t)/(81)})

expand

- \frac{2}{7} + \frac{lo g _{9} ( t )}{7} + \frac{6 lo g _{9} ( s )}{7}

Solution steps

Rewrite as

= lo g_{9} ((\frac{s ^{6} t}{81})^{\frac{1}{7}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{7} lo g_{9} (\frac{s ^{6} t}{81})

Simplify

lo g_{9} (\frac{s ^{6} t}{81}) : 6 lo g_{9} (s) + lo g_{9} (t) - 2

= \frac{1}{7} (6 lo g_{9} (s) + lo g_{9} (t) - 2)

Distribute parentheses

= \frac{1}{7} lo g_{9} (t) + \frac{1}{7} \cdot 6 lo g_{9} (s) + \frac{1}{7} (- 2)

Apply minus-plus rules

+ (- a) = - a

= \frac{1}{7} lo g_{9} (t) + 6 \cdot \frac{1}{7} lo g_{9} (s) - 2 \cdot \frac{1}{7}

6 \cdot \frac{1}{7} lo g_{9} (s) = \frac{6}{7} lo g_{9} (s)

2 \cdot \frac{1}{7} = \frac{2}{7}

= \frac{1}{7} lo g_{9} (t) + \frac{6}{7} lo g_{9} (s) - \frac{2}{7}

Multiply

\frac{1}{7} lo g_{9} (t) : \frac{lo g _{9} ( t )}{7}

= \frac{lo g _{9} ( t )}{7} + lo g_{9} (s) \frac{6}{7} - \frac{2}{7}

Multiply

lo g_{9} (s) \frac{6}{7} : \frac{6 lo g _{9} ( s )}{7}

= \frac{lo g _{9} ( t )}{7} + \frac{6 lo g _{9} ( s )}{7} - \frac{2}{7}

Combine the fractions

\frac{lo g _{9} ( t )}{7} + \frac{6 lo g _{9} ( s )}{7} : \frac{lo g _{9} ( t ) + 6 lo g _{9} ( s )}{7}

= - \frac{2}{7} + \frac{6 lo g _{9} ( s ) + lo g _{9} ( t )}{7}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 + lo g _{9} ( t ) + 6 lo g _{9} ( s )}{7}

- 2 + lo g_{9} (t) + 6 lo g_{9} (s) = - 2 + lo g_{9} (t s^{6})

= \frac{- 2 + lo g _{9} ( s ^{6} t )}{7}

lo g_{9} (t s^{6}) = lo g_{9} (t) + 6 lo g_{9} (s)

= \frac{- 2 + lo g _{9} ( t ) + 6 lo g _{9} ( s )}{7}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 2 + lo g _{9} ( t ) + 6 lo g _{9} ( s )}{7} = - \frac{2}{7} + \frac{lo g _{9} ( t )}{7} + \frac{6 lo g _{9} ( s )}{7}

= - \frac{2}{7} + \frac{lo g _{9} ( t )}{7} + \frac{6 lo g _{9} ( s )}{7}

\frac{2}{9 + 4 x}

(x^{3} - 2) (sec^{2} (x))

e^{in (s e c (θ) + t a n (θ))}

\frac{1}{( 1 - e ^{x} )}

- \frac{( x + α t ) ^{2}}{2}

What is expand log_{9}(\sqrt[7]{(s^6t)/(81)}) ?
The solution to expand log_{9}(\sqrt[7]{(s^6t)/(81)}) is -2/7+(log_{9}(t))/7+(6log_{9}(s))/7