Question

Solve for x. I will post it equation form in the comments
(2)5^(2x-9) -250

Answer 1

\[(2)5^{2x-9} - 250\]

Answer 2

Is that - an =, or is this being equated to 0 (essentially equivalent), or something else?

Answer 3

sorry is an = sign my printer didnt print it off right

Answer 4

\[(2)5^{2x-9} = 250\]

Answer 5

Alright. Obvious first step: divide through by 2. Then tell me if you can think of anything that you can do to terms in the form a^x, for example.

Answer 6

sorry so do you mean 250/2. hmmm, I think it has something to do with using log because thats the opposite of exponents correct?

Answer 7

I am not exactly sure what you mean by using a^x

Answer 8

Yeah, I was simply alluding to logs. What base should you take logs in, looking at the left hand side (5 raised to a function of x) and the right hand side (125)?

Answer 9

i think its 5, but I keep having trouble with this because I dont have a good understanding of using bases. I was reading that my calculator only takes bases of 10

Answer 10

Yes, it is 5. Your calculator may only calculate logarithms in base 10 and e, but that doesn't matter, since you don't need to use your calculator for this question.

Answer 11

\[5^{2x - 9} = 125 \to (2x-9)\log_5{5} = \log_5{125}\]By the log relationship:\[\log{a^b} = b \log{a}\]

Answer 12

so would I come to the equation (2x-9)5 = 5^3?

Answer 13

You can't simply get rid of the logs. I have taken the log (base 5) of both sides. By the relationship I noted, the right side would be 3log(5). You should also note that log(5) (where log is in base 5) is 1.

Answer 14

but how would you break it down to solve for x?

Answer 15

Noting that log base 5 of 5 is 1, the version of the equation I posted simplifies to:\[(2x - 9) = 3\]I imagine you can solve this by yourself. I have to leave now, so I can't provide further elaboration on the working of logs, but if you still don't get it I'm sure somebody else can fill you in.

Answer 16

okay thank you!