Rewrite as an equation.

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>9</mn></mrow></msub><mrow><mo>(</mo><mn>27</mn><mo>)</mo></mrow><mo>=</mo><mi>x</mi></mstyle></math> in exponential form using the definition of a logarithm. If <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> are positive real numbers and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> does not equal <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> , then <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>y</mi></mstyle></math> is equivalent to <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mi>y</mi></mrow></msup><mo>=</mo><mi>x</mi></mstyle></math> .

Create expressions in the equation that all have equal bases.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mi>x</mi></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn><mi>x</mi></mrow></msup></mstyle></math> .

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

Solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

The variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> is equal to <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Mixed Number Form:

Do you know how to Evaluate log base 9 of 27? 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 | one billion five hundred fifty million sixty-nine thousand three hundred eighty-six |
---|

- 1550069386 has 8 divisors, whose sum is
**2331338724** - The reverse of 1550069386 is
**6839600551** - Previous prime number is
**373**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | one billion five hundred forty-eight million six hundred fourteen thousand one hundred thirty-three |
---|

- 1548614133 has 32 divisors, whose sum is
**2309523840** - The reverse of 1548614133 is
**3314168451** - Previous prime number is
**19**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 36
- Digital Root 9

Name | five hundred eight million seven hundred twenty-six thousand six hundred seventeen |
---|

- 508726617 has 16 divisors, whose sum is
**778227072** - The reverse of 508726617 is
**716627805** - Previous prime number is
**257**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 42
- Digital Root 6