Expand the Logarithmic Expression log base b of ninth root of (x^4)/(y^9x^5)

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$\log_{b} (\sqrt[9]{\frac{x^{4}}{y^{9} x^{5}}})$

Rewrite $\sqrt[9]{\frac{x^{4}}{y^{9} x^{5}}}$ as ${(\frac{x^{4}}{y^{9} x^{5}})}^{\frac{1}{9}}$ .

$\log_{b} ({(\frac{x^{4}}{y^{9} x^{5}})}^{\frac{1}{9}})$

Expand $\log_{b} ({(\frac{x^{4}}{y^{9} x^{5}})}^{\frac{1}{9}})$ by moving $\frac{1}{9}$ outside the logarithm.

$\frac{1}{9} \log_{b} (\frac{x^{4}}{y^{9} x^{5}})$

Reduce the expression $\frac{x^{4}}{y^{9} x^{5}}$ by cancelling the common factors.

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Multiply by $1$ .

$\frac{1}{9} \log_{b} (\frac{x^{4} \cdot 1}{y^{9} x^{5}})$

Factor $x^{4}$ out of $y^{9} x^{5}$ .

$\frac{1}{9} \log_{b} (\frac{x^{4} \cdot 1}{x^{4} (y^{9} x)})$

Cancel the common factor.

$\frac{1}{9} \log_{b} (\frac{x^{4} \cdot 1}{x^{4} (y^{9} x)})$

Rewrite the expression.

$\frac{1}{9} \log_{b} (\frac{1}{y^{9} x})$

Rewrite $\log_{b} (\frac{1}{y^{9} x})$ as $\log_{b} (1) - \log_{b} (y^{9} x)$ .

$\frac{1}{9} (\log_{b} (1) - \log_{b} (y^{9} x))$

Logarithm base $b$ of $1$ is $0$ .

$\frac{1}{9} (0 - \log_{b} (y^{9} x))$

Subtract $\log_{b} (y^{9} x)$ from $0$ .

$\frac{1}{9} (- \log_{b} (y^{9} x))$

Rewrite $\log_{b} (y^{9} x)$ as $\log_{b} (y^{9}) + \log_{b} (x)$ .

$\frac{1}{9} (- (\log_{b} (y^{9}) + \log_{b} (x)))$

Expand $\log_{b} (y^{9})$ by moving $9$ outside the logarithm.

$\frac{1}{9} (- (9 \log_{b} (y) + \log_{b} (x)))$

Apply the distributive property.

$\frac{1}{9} (- (9 \log_{b} (y)) - \log_{b} (x))$

Multiply $9$ by $- 1$ .

$\frac{1}{9} (- 9 \log_{b} (y) - \log_{b} (x))$

Apply the distributive property.

$\frac{1}{9} (- 9 \log_{b} (y)) + \frac{1}{9} (- \log_{b} (x))$

Cancel the common factor of $9$ .

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Factor $9$ out of $- 9 \log_{b} (y)$ .

$\frac{1}{9} (9 (- \log_{b} (y))) + \frac{1}{9} (- \log_{b} (x))$

Cancel the common factor.

$\frac{1}{9} (9 (- \log_{b} (y))) + \frac{1}{9} (- \log_{b} (x))$

Rewrite the expression.

$- \log_{b} (y) + \frac{1}{9} (- \log_{b} (x))$

Combine $\frac{1}{9}$ and $\log_{b} (x)$ .

$- \log_{b} (y) - \frac{\log_{b} (x)}{9}$

Do you know how to Expand the Logarithmic Expression log base b of ninth root of (x^4)/(y^9x^5)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	nine hundred seventy-nine million fifty-one thousand six hundred sixty-one

Interesting facts

979051661 has 8 divisors, whose sum is 1133080320
The reverse of 979051661 is 166150979
Previous prime number is 79

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 44
Digital Root 8

Name

Name	one billion four hundred twenty-five million three hundred eighty-nine thousand three hundred ninety-six

Interesting facts

1425389396 has 64 divisors, whose sum is 3396556800
The reverse of 1425389396 is 6939835241
Previous prime number is 359

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 50
Digital Root 5

Name

Name	three hundred twenty-nine million two hundred fifty-nine thousand nine hundred fifty-seven

Interesting facts

329259957 has 32 divisors, whose sum is 485388288
The reverse of 329259957 is 759952923
Previous prime number is 263

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 51
Digital Root 6

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