how do you solve 5^t=11^5+t?

Question

please help! ASAP

Answer 1

Here is an instance where you must use a logarithm in order to isolate the variable. Try using log base 10 its usually the easiest and is always denoted just log.
In this case taking a log would result in:
5^t=11^5+t
The log will bring the exponent down in front like so:
t(log5)=(5+t)log11
Now distribute on the right:
tlog5=5log11+tlog11
Now reverse sides:
-5log11=tlog11-tlog5
Factor out the t:
-5log11=t(log11-log5)
Now get a general idea of log11-log5:
-5log11=t(.3424226)
Now divide -5log11 by .3424226
-15.20624572=t

Answer 2

set the equation equal to zero and then use the quadratic formula which is right here:

http://www.gomath.com/htdocs/images/4-3-03(1).gif

unless it is 11^(5+t), in which case that logarithmic answer above is probably right

Answer 3

5^t=11^5+t

t log 5 = (t + 5)log 11

t/(t + 5) = log 11/log 5

t/(t + 5) = log 11/log 5

t/(t + 5) = 1.49

t = 1.49(t + 5)

t - 1.49t = 7.45

-0.49t =7.45

t = -15.2
.

Answer 4

the answer is 7 duh i am a mathematics professor Just playin !! goodluck