How do you solve this: 3^(4x)=5^(x-1) without using a calculator...

Can someone please explain how you solve this.. it would be very helpful!

Lets try logarithms:

you can use it with any base if logs.

log(3^4x) = log(5^[x-1])
4x*log3 = (x-1)log5
4x*log3 = x*log5 - log5

4x*log3 - x*log5 = - log5

x(4log3-log5) = -log5:
x = -log5/(4log3-log5)

Now if we say that log is the logarithm with base of 5 the answer may be simplified to :

x = -1/(4*log3 - 1)

Taking the base-10 logarithm of both sides, we get:

4x•log(3) = (x-1)•log(5)
4x = (x-1)•[(log(5))/(log(3))]
4x = (x-1)•[log_3(5)]

Use a calculator to evaluate the right-hand side logarithm now. The rest is simple algebraic manipulation. I think you can do it.

Hello GAVEN, may I use logarithm?
Taking log to the base 10, we get 4x log3 = (x-1)*log 5
From the tables meant for logarithm
log 3 = 0.4771 and log5 = 0.6990
Now x(log5-4log3) = log5
So x = log 5 /(log5 - 4 log3)
Any way x would be negative.