Question

Please Help! using natural Logarithms to solve exponential equations
See Attachment

Answer 1

Do you have to use natural logs? This could be done with common (base 10) logs?

Answer 2

I'm not sure, but I can try

Answer 3

Okay - I think I could solve it with natural logs, but common logs are much easier to understand.
Well, this will be done with common logs.

Answer 4

ok

Answer 5

6^(t+1) = 7^t
Taking logs of both sides
(t+1) * log (6) = t * log (7)
(t+1) * 0.7781512504 = t * 0.84509804
(t+1) / t = 0.84509804 / 0.7781512504
(t+1) / t = 1.0860331325

(t+1)/t = 1 + 1/t

1/t = 1.0860331325 -1
1/t = .0860331325
t = 11.6234289154

Double Check
6^(12.6234289154) = 7^11.6234289154
6,651,766,485 = 6,651,766,485

Answer 6

It says that it is incorrect, but thank you!

Answer 7

The answer is t = 11.6234289154
Did you input that?

Answer 8

yes

Answer 9

Can you assist me with another one?

Answer 10

Even though the last answer I gave was wrong?
Okay I'll give this one a try.

Answer 11

ln(x) = 11/7
ln(x) = 1.5714285714
x = e^1.5714285714
x = 4.8135197393
x = 4.814 (rounded to 3 decimal places)