Question

I need help understanding what I did wrong. (explanation below)

Answer 1

Find the exact solution to the equation: 5^(6-2x) = 25.

What I did was start by logging both sides. Then use the exponential property of log so the equation becomes (6-2x) log 5 = log 25. I then distribute so the equation becomes 6log 5 - 2xlog 5 = log 25. I kept the expression with the variable on one side, so I subtracted the 6log 5. The equation is now -2x log 5 = log 25 - 6log 5. I then factor out the x so it's by itself and divide the -2log5 on both sides. The equation is now x = (log 25 - 6log 5) / -2 log 5. The answer I got was like .977 something but the solution is actually either 2, 3, 5, or -2.

The log is considered log_10 so I didn't bother writing that part out. Can someone please explain to me what I did wrong? I followed the guidelines they gave us in the book so I'm confused on when I made the error. Thank you!

Answer 2

what is log(25)/log(5) ?

Answer 3

for that matter

if we know that 5^n = 25 ... what would you determine 'n' to be?

Answer 4

log 25 / log 5 = 2. So if 5^n = 25 then n also is 2. What happens to the (6-2x) part of the equation though?

Answer 5

n = 6-2x doesnt it? but n=2

Answer 6

Oh okau. So 2 = 6 - 2x
-4 = -2x
2 = x so x ALSO is 2

Answer 7

but as far as your own approach ....

(6-2x) log(5) = log(25)

6 log(5) -2x log(5) = log(25)

6 log(5) - log(25) = 2x log(5)

6 log(5)/(2log(5)) - log(25)/2(log(5)) = x

6 log(5)/(2log(5)) - log(25)/2(log(5)) = x

log(5)/log(5) = 1 , soo that term is 3

3 - log(25)/(2log(5)) and the next terms is 2, divided by 2 = 1

3 - 1 = x

Answer 8

i just think its simpler to deal with n = 6-2x = 2 :)

Answer 9

Yeah that makes much sense. Hopefully on the test I can just do it that way cause using all the steps is confusing. Thank you so much!

Answer 10

good luck :)