Question

@zordoloom

7^t=8^t+1

Answer 1

Ok, start by taking the ln or log of both sides.

Answer 2

that seems to be the part i keep getting stuck on

i end up with tlog7=tlog8+log8

Answer 3

ok, Let me write out the steps then.

Answer 4

Okay thanks

Answer 5

Actually know what. let me take a different approach.

Answer 6

Divide both sides by 7^t

Answer 7

So, 1=(8^(t+1))/(7^t)

Answer 8

ok

Answer 9

Now if you rewrite (8^(t+1))/(7^t), rewrite it as 7^-t(8^(t+1)=1

Answer 10

Are you following so far?

Answer 11

Um yeah i think so

Answer 12

Where at?

Answer 13

Are you confused.

Answer 14

So the t is now negative on the 7 because we're dividing right?

Answer 15

Its negative because it moved from denominator to numerator.

Answer 16

Okay i gotcha now

Answer 17

Now, you want a common base. So raise both sides by e and take the log of both sides. Let me show you what i mean.

Answer 18

e^((log(8)(t+1)-tlog(7))=1

Answer 19

now take the ln of both sides.

Answer 20

Now combine in terms of t

t(ln(8)-ln(7))+ln(8)=0

Answer 21

so, t=(-ln8)/(ln8-ln7))

Answer 22

Okay let me see if i get the correct answer

Answer 23

ok

Answer 24

Okay so when i punched it in i got -15.57

is that correct or does it just remain t=(-ln8)/(ln8-ln7))

Answer 25

Both would be correct.

Answer 26

Okay great! thanks again...

Answer 27

If you want exact form, use the fraction looking example, if you want approximate, use the decimal.

Answer 28

I'll probably end up using the exact form just in case

Answer 29

Thats a good choice. Thats what i would leave it in.

Answer 30

Best response?