$\text{Use}\ \log_ab=c\iff a^c=b,\ \text{for}\ a>0,\ b>0\ \wedge\ a\neq1\\\\Domain:b>0\ \wedge\ b\neq1\\\\\log_b(512)=3\iff b^3=512\to b=\sqrt[3]{512}\\\\\begin{array}{c|c}512&2\\256&2\\128&2\\64&2\\32&2\\16&2\\8&2\\4&2\\2&2\\1\end{array}\\\\512=2^9=2^{3\cdot3}=(2^3)^3=8^3\\\\\text{Therefore}\ b=\sqrt[3]{512}=\sqrt[3]{8^3}=8\in D$

$\text{Used:}\\\\(a^n)^m=a^{nm}\\\\\sqrt[n]{a^n}=a$

6 0

3 years ago

Which numbers are rational And which are irrational

Fittoniya [83]

Answer:

Irrational, rational, rational, rational, irrational

Step-by-step explanation:

Pi is irrational, so anything multiplied by it is irrational also. The square root of 25 is just 5 or -5, both of which are rational. 17/12 is a fraction of integers so it's rational. 41.4141... is a repeating decimal so it is rational. And the square root of 7 is a random decimal, so it is irrational.

8 0

3 years ago

HELP plzzzzzzzzzzzzzzzz

tia_tia [17]

Answer:

b i think

Step-by-step explanation:

7 0

3 years ago

There are 12 ice cream cups in a box if the box cost 9.60 how much does each cup of ice cream cost

larisa86 [58]

You would take the number of ice cream cups which is 12 and divide it by the cost which is 9.60
12/9.60=1.25