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

Rewrite <math><mstyle displaystyle="true"><mroot><mrow><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mfrac></mrow><mrow><mn>9</mn></mrow></mroot></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mfrac><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Expand <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mo>(</mo><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mfrac><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mstyle></math> by moving <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> outside the logarithm.

Multiply by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></msup></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><mi>x</mi></mrow></mfrac><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Logarithm base <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><mi>x</mi><mo>)</mo></mrow></mstyle></math> from <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><mi>x</mi><mo>)</mo></mrow></mstyle></math> as <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><mo>)</mo></mrow><mo>+</mo><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>9</mn></mrow></msup><mo>)</mo></mrow></mstyle></math> by moving <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> outside the logarithm.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Apply the distributive property.

Factor <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>9</mn><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

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 | three hundred eleven million seven hundred forty-five thousand two hundred twenty-two |
---|

- 311745222 has 64 divisors, whose sum is
**854219520** - The reverse of 311745222 is
**222547113** - Previous prime number is
**641**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 27
- Digital Root 9

Name | one billion one hundred ninety-three million four hundred forty-seven thousand seven hundred thirty-five |
---|

- 1193447735 has 8 divisors, whose sum is
**1462608576** - The reverse of 1193447735 is
**5377443911** - Previous prime number is
**47**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 44
- Digital Root 8

Name | five hundred thirteen million four hundred nineteen thousand two hundred thirty-two |
---|

- 513419232 has 256 divisors, whose sum is
**5203835280** - The reverse of 513419232 is
**232914315** - Previous prime number is
**4409**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 30
- Digital Root 3