Question

7^t=8^t+1
solve for t

Answer 1

anyone know?

Answer 2

Is it 7^t = (8^t) + 1
or 7^t = 8^(t+1).... this one meaning the t+1 is the whole exponent.

Answer 3

because the second one is much easier to solve.. I don't know how to solve the first one

Answer 4

\[1)7^t=8^t+1\]
or
\[2)7^t=8^{t+1}\]

Answer 5

If it's the second one I can help:
Basically when you see exponents, you usually have to solve for them using logarithms (usually we tend to log both sides):

\[\ln7^t=\ln(8^{t+1})\]\[ln7^t=\ln(8^t*8^1)\]\[\ln7^t=\ln8^t+\ln8\]\[\ln7^t-\ln8^t=\ln8\]\[\ln(7^t/8^t)=\ln8\]\[\ln((7/8)^t)=\ln8\]\[t*\ln(7/8)=\ln8\]\[t=\frac{ \ln8 }{ \ln(7/8) }\]\[t=\frac{\ln8}{\ln7-\ln8}\]

Answer 6

if you want you can simplify ln8 as 3*ln(2), because 8 = 2^3
So, ln(8) = ln(2^3) = 3*ln(2)