Can someone please solve for "t" step by step in this problem?

Question

7*3^t=5*2^t

I tried but it seems like t always cancels out... Thanks

Answer 1

Divide both sides by 5, then by 3^t

7/5 = 2^t / 3^t

which can be rewritten as 7/5 = (2/3)^t

Now just take the log (with a base of 2/3) and you get

log(base 2/3) 7/5 = t

you can do that on a calculator by typing in

[log (7/5)]/[log(2/3)]

Answer 2

In fact, t does not cancel out.

It easiest to take logarithms of both sides (bases don't matter). Multiplication becomes addition, and the exponent becomes a multiplication factor.

So 7 . 3^t = 5 . 2^t becomes

log 7 + t log 3 = log 5 + t log 2,

and you can solve this for t. Algebraically,

(log 3 - log 2) t = (log 5 - log 7), so
t = (log 5 - log 7) / (log 3 - log 2)

Numerically,

0.8451 + 0.4771 t = 0.6990 + 0.3010 t
t = -0.8298

Check:
7 . 3^(-0.8298) = 2.8131
5 . 2^(-0.8298) = 2.8130
which (apart from small rounding error) shows that this is indeed a solution.

Answer 3

You're doing it wrong. If you had 3^4/2^4, it is not 3/2. Rearrange to 3^t / 2^t = 5/7, and convert to logs to get t log 3 - t log 2 = log (5/7) and then
t= log (5/7) / [log 3 - log 2]

Answer 4

You have to treat the numbers with exponents like a single term. Get the terms with t on one side of the equation. Get the terms without t on the opposite side. Take the LOG of both sides to reduce the equation to a linear form. Note that you probably already know things like LOG(3^t) = t*LOG(3). And, LOG(x/y) = LOG(x)-LOG(y). You will be able to factor out a t and then simplify by dividing both sides by LOG(x)-LOG(y).

Answer 5

7*3^t=5*2^t
or,3^t/2^t=5/7
or,(3/2)^t=5/7
or,t=ln(5/7)/ln(3/2)
or,t=...... please press ur calculator. and check keeping the value of t