Question

solve:
5^(2x)=3

Answer 1

take the log of both sides.
divide both sides by log(5).
divide both sides by 2.

Answer 2

need help?

Answer 3

just a bit, trying your method but not connecting the dots

Answer 4

\[\log_5(5^{(2x)})=\log_5(3)\]
\[\text{ So this is step we took } log_5() \text{ of both sides }\]
Now what properties do you know about log?
What properties of log could we find useful here?

Answer 5

We didn't have to choose log base 5
We could have done what dpalnc went with
I also like to use log base e or natural log
I just chose log base 5
because I knew log base 5 of 5 is 1

So if you don't like that we could do ln( ) of both side
Whatever!
:)
\[\ln(5^{(2x)})=\ln(3)\]
But still the reason we use natural log is so we can do what with that exponent part?
Like that exponent part contains the thing we want to solve for
What is the point int taking log of both sides
What property of log will we use here that will get us on our way to solving for x

Answer 6

Here is a list of some properties of log:
\[a,b,x>0\]
\[\ln(ab)=\ln(a)+\ln(b) \]
\[\ln(\frac{a}{b})=\ln(a)-\ln(b)\]
\[\ln(x^r)=r \ln(x)\]
\[\ln(1)=0\]
\[\ln(e)=1\]

Answer 7

What property that I have listed will be of use here?

Answer 8

sorry ive been stuck in the book... so far i did this
\[5^{2x}=3\]
\[\log5^{2x}=\log3\]
\[2xlog5=\log3\]
\[\log3/2\log5 = 0.167\]

Answer 9

How exactly did you enter that into the calculator?

Answer 10

incorrectly...sorry catching up slowly...

Answer 11

lol... Ok. I'm glad you notice.
But the exact answer looks good
Good job on that part
The only thing bad is your approximation

Answer 12

Well I would have said your answer like this:
log3/(2log5)

Answer 13

But I know what you meant