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

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Algebra

$2 (\log_{3} (8) + \log_{3} (z)) - \log_{3} (3^{4} - 7^{2})$

Simplify each term.

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Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$2 \log_{3} (8 z) - \log_{3} (3^{4} - 7^{2})$

Simplify $2 \log_{3} (8 z)$ by moving $2$ inside the logarithm.

$\log_{3} ({(8 z)}^{2}) - \log_{3} (3^{4} - 7^{2})$

Apply the product rule to $8 z$ .

$\log_{3} (8^{2} z^{2}) - \log_{3} (3^{4} - 7^{2})$

Raise $8$ to the power of $2$ .

$\log_{3} (64 z^{2}) - \log_{3} (3^{4} - 7^{2})$

Simplify each term.

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Raise $3$ to the power of $4$ .

$\log_{3} (64 z^{2}) - \log_{3} (81 - 7^{2})$

Raise $7$ to the power of $2$ .

$\log_{3} (64 z^{2}) - \log_{3} (81 - 1 \cdot 49)$

Multiply $- 1$ by $49$ .

$\log_{3} (64 z^{2}) - \log_{3} (81 - 49)$

Subtract $49$ from $81$ .

$\log_{3} (64 z^{2}) - \log_{3} (32)$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{3} (\frac{64 z^{2}}{32})$

Cancel the common factor of $64$ and $32$ .

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Factor $32$ out of $64 z^{2}$ .

$\log_{3} (\frac{32 (2 z^{2})}{32})$

Cancel the common factors.

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Factor $32$ out of $32$ .

$\log_{3} (\frac{32 (2 z^{2})}{32 (1)})$

Cancel the common factor.

$\log_{3} (\frac{32 (2 z^{2})}{32 \cdot 1})$

Rewrite the expression.

$\log_{3} (\frac{2 z^{2}}{1})$

Divide $2 z^{2}$ by $1$ .

$\log_{3} (2 z^{2})$

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

Name	one billion thirty-six million four hundred thirty thousand six hundred twenty-nine

Interesting facts

1036430629 has 8 divisors, whose sum is 1123549952
The reverse of 1036430629 is 9260346301
Previous prime number is 151

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 34
Digital Root 7

Name

Name	two billion twenty-one million five hundred forty-six thousand six hundred seventy-eight

Interesting facts

2021546678 has 8 divisors, whose sum is 3045334968
The reverse of 2021546678 is 8766451202
Previous prime number is 233

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 41
Digital Root 5

Name

Name	six hundred seventy million six hundred one thousand seven hundred twenty-two

Interesting facts

670601722 has 8 divisors, whose sum is 1149602976
The reverse of 670601722 is 227106076
Previous prime number is 7

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 31
Digital Root 4

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