admissions practice test

[siciliantycoon]

7. If log ^10x + log ^10 y =3, then xy =

the answer is 1000, but im wondering how to find that

and....

3. ?3 + ?27= 4?3

how do you get that answer? i figured it out to be 6, but i was wrong

 

[Deleted member 4993]

I think your problem statement is:
\(\displaystyle If\)

\(\displaystyle Log_{10}(x) + Log_{10}(y) = 3\)

\(\displaystyle then\)

\(\displaystyle xy = ??\)

Use the definition

\(\displaystyle Log_{a}(m) + Log_{a}(n) = m \cdot\ n\)

and

\(\displaystyle If\)

\(\displaystyle Log_{a}(m) = p\)

then

\(\displaystyle a^p = m\)

 

[soroban]

Hello, siciliantycoon!

If you'd show your work, we could be more effective . . .

\(\displaystyle 3)\;\;\sqrt{3} + \sqrt{27} \:=\:4\sqrt{3}\)

\(\displaystyle \text{We are expected to simplify: }\;\sqrt{27} \:=\:\sqrt{9\cdot3} \:=\:\sqrt{9}\cdot\sqrt{3} \:=\:3\sqrt{3}\)

\(\displaystyle \text{The problem becomes: }\;\sqrt{3} + 3\sqrt{3} \;=\;\boxed{4\sqrt{3}}\)

. . . \(\displaystyle (\text{This is the same as: }\;a + 3a \:=\:4a)\)