# Thread: Possibly a change of base rule log problem

1. ## Possibly a change of base rule log problem

I guessing I have to use a change of base rule for this but then I got stuck because it might not be a change of base rule.

2. ## Re: Possibly a change of base rule log problem

do us a favor and type out your problem ...

3. ## Re: Possibly a change of base rule log problem

If (log base of b x) multiplied by (log base of 2 b)=3 what is the value of x?

4. ## Re: Possibly a change of base rule log problem

Originally Posted by dtdj13
If (log base of b x) multiplied by (log base of 2 b)=3 what is the value of x?
$\log_b{x} \cdot \log_2{b} = 3$

change of base for the first factor ...

$\dfrac{\log_2{x}}{\log_2{b}} \cdot \log_2{b} = 3$

can you finish?

5. ## Re: Possibly a change of base rule log problem

i honestly can not finish it because this is a new concept to me and I couldn 't find a example in my math book like this. can you work out a problem like this or just show me the steps on how to complete it?

btw my professor told my last chance of getting help, the tutors at my school not to help the students. He said to get help from other sources.

6. ## Re: Possibly a change of base rule log problem

$\dfrac{\log_2{x}}{\cancel{\log_2{b}}} \cdot \cancel{\log_2{b}} = 3$

$\log_2{x} = 3$

change the log equation to an exponential equation to find the value of $x$.

7. ## Re: Possibly a change of base rule log problem

log base of b (x)= 3/log base of 2 (b)

3/log base of 2 (b)= log base of b (b3/logbase 2 (b))

log base of b (x) = log base of b (b3/logbase 2 (b))

then the logs have the same base

log base of b (x) (3/blog base of 2 (b))

=3/b log base of 2 (b)

8. ## Re: Possibly a change of base rule log problem

Originally Posted by dtdj13
log base of b (x)= 3/log base of 2 (b)

3/log base of 2 (b)= log base of b (b3/logbase 2 (b))

log base of b (x) = log base of b (b3/logbase 2 (b))

then the logs have the same base

log base of b (x) (3/blog base of 2 (b))

=3/b log base of 2 (b)
what is all that? ... did you not read my last post?

$\log_2{x} = 3$

change the log equation to an exponential equation ...

$x = 2^3 = 8$

... you're done.