Set the argument of the logarithm equal to zero.

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

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from both sides of the equation.

Divide each term by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>4</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Move the negative in front of the fraction.

The vertical asymptote occurs at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the expression.

Simplify the result.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Logarithm base <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to decimal.

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> in the expression.

Simplify the result.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>24</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Logarithm base <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> of <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Rewrite as an equation.

Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>5</mn></mrow></msub><mrow><mo>(</mo><mn>25</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 equivalent expressions in the equation that all have equal bases.

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

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

The final answer is <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Convert <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to decimal.

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> in the expression.

Simplify the result.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>5</mn></mrow></msub><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mstyle></math> .

Convert <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mn>5</mn></mrow></msub><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mstyle></math> to decimal.

The log function can be graphed using the vertical asymptote at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> and the points <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>6</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1.36521238</mn><mo>)</mo></mrow></mstyle></math> .

Vertical Asymptote: <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

Do you know how to Graph f(x) = log base 5 of 4x+1? 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 six hundred forty-six million nine hundred ninety-two thousand six hundred three |
---|

- 1646992603 has 4 divisors, whose sum is
**1647326808** - The reverse of 1646992603 is
**3062996461** - Previous prime number is
**5003**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | four hundred twenty-seven million nine hundred twenty-seven thousand six hundred sixty |
---|

- 427927660 has 64 divisors, whose sum is
**1201404960** - The reverse of 427927660 is
**066729724** - Previous prime number is
**67**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 43
- Digital Root 7

Name | two billion one million four hundred forty-three thousand six hundred forty-four |
---|

- 2001443644 has 16 divisors, whose sum is
**4504711968** - The reverse of 2001443644 is
**4463441002** - Previous prime number is
**3137**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 28
- Digital Root 1