Question

9=(sqrt of 3) ^ (4x+6)... Can someone please explain their method/strategy as well? I don't understand.

Answer 1

\[(\sqrt{3})^{4x+6} = 9\]
you can take log of both sides
\[\log \sqrt{3})^{4x+6} = \log 9\]
\[(4x+6)(\log \sqrt{3}) = \log 9\]
\[4x + 6 = \frac{\log 9}{\log \sqrt{3}} = 4\]

Answer 2

that is one way. without the log you can say
\[\sqrt{3}^2=3\] so
\[\sqrt{3}^4=9\] and therefore
\[4x+6=9\] etc

Answer 3

Thanks!! Both of you, yeah I needed to do it without the log.

Answer 4

oh ok, yeah mine is the formal way which will always work
cause what if it was sqrt(2) then you have to use log

Answer 5

Yeah, I am probably going to learn log next.. Hopefully I'll understand that.. Thanks though

Answer 6

no problem

Answer 7

One more question...

Answer 8

?

Answer 9

If I were to explain the steps of how I did this, I'd say I created equal bases and the solved for the variable and got x=3/4

Answer 10

yes, by getting equal bases you can set the exponents equal to each other and then solve for the variable.

i get x = -1/2 for this problem

Answer 11

Wait how did you get -1/2

Answer 12

4x+6 = 4
4x = -2
x = -2/4 = -1/2

Answer 13

satellite had a typo at the end
since 9 can be written as sqrt(3)^4
the equal base is sqrt(3)
exponents are (4x+6) on left and 4 on right

4x+6 = 4