I have two math problems that seem easy but they are actually evil. HELP!

1) Solve for t:

30(0.85^t)=60

2) Solve for t:

7^t=8^t+1

Thank you in advance!

First, it's easier to deal with separate questions in separate posts, but I'll deal with these:

1) Divide both sides by 30 to get
(0.85^t) = 2
Take log of both sides
log (0.85^t) = log 2
Use properties of logs
t log (0.85) = log 2
and divide
t = (log 2)/(log 0.85)

2) I have to assume you mean 7^t = 8^(t+1),
since their is no solution to 7^t = (8^t) + 1

Take log of both sides
log (7^t) = log (8^(t+1))
Use properties of logs
t log 7 = (t+1) log 8
Distribute
t log 7 = t log 8 + log 8
t log 7 - t log 8 = log 8
t (log 7 - log 8) = log 8
t = (log 8)/(log 7 - log 8)

3) Use properties of logs to rewrite left side of equation
log (4t^2) = 2
Exponentiate both sides to the power of 10
10^(log(4t^2)) = 10^2
Simplify
4t^2 = 100
t^2 = 25
t = 5

1.

30(0.85^t)=60             given
0.85^t = 2                   divide both sides of "=" by 30
ln(0.85^t) = ln(2)         take logs of both sides of "="
t·ln(0.85) = ln(2)          ln(aⁿ) = nln(a)
t = ln(2)/ln(0.85)          simplify
t ≈ -4.26502428          According to google


2.

7^t=8^t + 1                 given


3.

2log(t)+log(4)=2          given
log(4t²) = log(100)       assuming base 10 (logs)
4t² = 100
t² = 25
t = 5


The library I am at is closing, so, I didn't get to #2. I hope what I have helps. I'd like to know how to figure #2; e-mail me if you want. Good luck!

1. 30(0.85)^t = 60
take ln both sides
ln[30(0.85)^t] = ln60
ln30+t*ln(0.85) = ln(30*2) = ln30+ln2
t*ln(0.85) = ln2
t = ln2/ln(0.85)
t = -4.265(approx)

2. 7^t = 8^t+1
'+1' is the disturbing element!
Wait!

Tell your teacher you slept through the lecture on the quadracti equation.

Those problems are very easy for anyone who was awake in class.

I think u have to apply the distributive property.