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

Solve Math

Algebra

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

Simplify each term.

Tap for more steps...

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.

Tap for more steps...

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 $32$ .

Tap for more steps...

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

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

Cancel the common factors.

Tap for more steps...

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 three hundred eighty-seven million six hundred twenty-three thousand one hundred twenty-six

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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

Name

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

Interesting facts

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

Basic properties

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

Evaluate (-5)^3

Solve by Completing the Square x^2-10x-4=0

Solve Using the Quadratic Formula 3x^2-2x-5=0

Solve Using the Square Root Property (x-3)^2=5

Factor x^3-x^2+x-1