Write as a Single Logarithm 2( log base 3 of 8+ log base 3 of z)- log base 3 of 3^4-7^2

Use the product property of logarithms, <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><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mi>y</mi><mo>)</mo></mrow></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mn>2</mn><msub><mi>log</mi><mrow><mn>3</mn></mrow></msub><mrow><mo>(</mo><mn>8</mn><mi>z</mi><mo>)</mo></mrow></mstyle></math> by moving <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> inside the logarithm.

Apply the product rule to <math><mstyle displaystyle="true"><mn>8</mn><mi>z</mi></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify each term.

Raise <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>49</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>49</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>81</mn></mstyle></math> .

Use the quotient property of logarithms, <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><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mi>y</mi></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>32</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>64</mn><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>32</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>32</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>2</mn><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Do you know how to Write as a Single Logarithm 2( log base 3 of 8+ log base 3 of z)- log base 3 of 3^4-7^2? 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 | one billion three hundred eighty-seven million six hundred twenty-three thousand one hundred twenty-six |
---|

- 1387623126 has 16 divisors, whose sum is
**2775670128** - The reverse of 1387623126 is
**6213267831** - Previous prime number is
**8681**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | three hundred forty million seven hundred seventy-eight thousand eight hundred ninety-seven |
---|

- 340778897 has 4 divisors, whose sum is
**341139696** - The reverse of 340778897 is
**798877043** - Previous prime number is
**947**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 53
- Digital Root 8

Name | two billion one hundred five million eight hundred three thousand three hundred twenty |
---|

- 2105803320 has 128 divisors, whose sum is
**11443869216** - The reverse of 2105803320 is
**0233085012** - Previous prime number is
**157**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 24
- Digital Root 6