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 four hundred seventy-one million one hundred fifty-two thousand nine hundred five |
---|

- 1471152905 has 8 divisors, whose sum is
**1795305600** - The reverse of 1471152905 is
**5092511741** - Previous prime number is
**59**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 35
- Digital Root 8

Name | seven hundred ninety-one million seven hundred sixty-one thousand three hundred sixty-five |
---|

- 791761365 has 32 divisors, whose sum is
**1440320640** - The reverse of 791761365 is
**563167197** - Previous prime number is
**43**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | nine hundred fifty-five million seven hundred ninety-six thousand five hundred sixty-six |
---|

- 955796566 has 4 divisors, whose sum is
**1433694852** - The reverse of 955796566 is
**665697559** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 58
- Digital Root 4