Question

3^(2x-5)=15

Answer 1

hit both sides with a log.
\[3^{(2x-5)}=15\]\[(2x-5)Log3=Log15\]\[(2x-5)=Log(15)/Log(3)\]can you do it now?

Answer 2

Yes!! thank you for your help!

Answer 3

Tell me what you get when you are done, to make sure you are correct.

Answer 4

If you have any difficulties, tell me I'll give you a good tip.

Answer 5

Would I use the quotient property for Log(15)/Log(3) to make it log(15)-log(3), or would it wind up as log(5)?

Answer 6

\[\log_b (a) = \log (a) / \log(b) \]
\[So,~~~~ \log(15)/\log(3) = \log_3(15) \]now it's going to be \[2x+5=\log_315\]
you can say Let (2x+5) = a to make it even easier

Answer 7

makes sense?

Answer 8

Yes, could you show me the next step please? I'm not sure where to go from here

Answer 9

OK,
\[Let~~~~2x+5=a~~~~~~~now~~~~i t's~~~~going~~~~t o~~~~be\]\[a=Log_315\]\[USE~~~~THE:~~~~~~~~\color{red} {Log_ab=c~~~~~->~~~~~a^c=b}\]

Answer 10

no don't use the red definition, sorry.

Answer 11

haha, it's fine! what should I do, then?

Answer 12

Let me think, I can;t believe I am stock.
I know that \[2x=Log_315-5\]\[x=\frac{Log_315-5}{2}\]all you have left is to simplify the right hand side.

Answer 13

Hmm, that's okay! this is only a practice problem and I have the major steps down

thank you anyway!

Answer 14

I think I know, hold on....

Answer 15

\[\log_315=Log_3(3 \times 5)=Log_33+Log_35=1+Log_35\]so it's now,
\[x=\frac{Log_35-4}{2}=\frac{Log_35}{2}-2\]

Answer 16

okay, thank you so much!

Answer 17

\[Log_35=1.465\]So,
\[x=0.7325-2=-1.2675≈ -1.27\]

Answer 18

Anytime!