Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow><mo>=</mo><mn>2</mn></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> <math><mstyle displaystyle="true"><mo>≠</mo></mstyle></math> <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> .

Take the <math><mstyle displaystyle="true"><mtext class="not-bold-word">(+2)th</mtext></mstyle></math> root of both sides of the <math><mstyle displaystyle="true"><mtext class="not-bold-word">equation</mtext></mstyle></math> to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Exclude the solutions that do not make <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow><mo>=</mo><mn>2</mn></mstyle></math> true.

Do you know how to Solve for x log base b of 25=2? 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 | four hundred eighty-six million four hundred fifty-eight thousand nine hundred twelve |
---|

- 486458912 has 128 divisors, whose sum is
**3698654400** - The reverse of 486458912 is
**219854684** - Previous prime number is
**839**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 47
- Digital Root 2

Name | two billion thirty-five million seventy-four thousand nine hundred forty-two |
---|

- 2035074942 has 64 divisors, whose sum is
**6053080320** - The reverse of 2035074942 is
**2494705302** - Previous prime number is
**9**

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

Name | one billion five hundred sixty-seven million four hundred thirty-one thousand eight hundred seventy-three |
---|

- 1567431873 has 32 divisors, whose sum is
**3206016000** - The reverse of 1567431873 is
**3781347651** - Previous prime number is
**149**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 45
- Digital Root 9