Rewrite as an equation.

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>4</mn></mrow></msub><mrow><mo>(</mo><mn>64</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>2</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>2</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"><mn>3</mn></mstyle></math> .

Do you know how to Evaluate log base 4 of 64? 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 | two hundred forty-nine million twenty thousand three hundred thirty-seven |
---|

- 249020337 has 4 divisors, whose sum is
**332027120** - The reverse of 249020337 is
**733020942** - Previous prime number is
**3**

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

Name | fifty-one million seven hundred seventy-five thousand nine hundred thirty-one |
---|

- 51775931 has 16 divisors, whose sum is
**58131360** - The reverse of 51775931 is
**13957715** - Previous prime number is
**157**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 38
- Digital Root 2

Name | one billion six hundred eighty-eight million five hundred sixty-seven thousand five hundred twenty-six |
---|

- 1688567526 has 32 divisors, whose sum is
**3803783520** - The reverse of 1688567526 is
**6257658861** - Previous prime number is
**73**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 54
- Digital Root 9