Question

use properties of logarithms to find the exact value of the expression.

9^(log(base9)1-log(base9)2)
type an integer or a simplified fraction.

Answer 1

I think:
\[x^{\log_x(a)} = a\]

I am not sure whether I am true or not..

Answer 2

If above one is right then:

We will have:
\[\log(a) - \log(b) = \log(\frac{a}{b})\]

use this firstly..

Answer 3

Here a = 1 and b = 2...

Can you use this formula??

Answer 4

so it will be \[9^{\log \frac{ 1 }{ 2 }}\]

Answer 5

well i mean log base 9

Answer 6

Yep but don't forget to write base 9..

So it will be:
\[\huge 9^{\log_9(\frac{1}{2})}\]

Okay..

Now use the first formula that I gave.

Answer 7

It is similar to \(x^{log_{x}(a)}\)..

Answer 8

\[9^{\log _{9}\frac{ 1 }{ 2 }}=\frac{ 1 }{ 2 }\]

Answer 9

Yep, according to me this should be the answer...

Answer 10

so it should be 1/2??

Answer 11

or the entire equation?

Answer 12

You have reduced entire expression to 1/2. That is it..!!

Answer 13

oh! okay thank you!!!!!

Answer 14

You are welcome dear...