How do i find the answer for y in problems such as 2^y = 256?

Question

is there a simple way to get the answer for y without having to multiply 2 over and over until you get 256?

please do not just post the answer.

Answer 1

Take log base 2 of both sides.
log2 (2^y) = log2 (256)
y log2 (2) = log2 (256)
y x 1 = 8
y = 8

Answer 2

If you only have a basic calculator, multiplying 2 over and over is probably the easiest way to do this.

If you have a more complex calculator, such as a TI-89, you can tell it:
Solve(2^y=256, y)
and it will solve the equation for y.

Answer 3

Basically, you want to get y by itself. The manner to do so is to either take logarithm or natural logarithm to each side of the equal sign. I'm going to use log in my sample below, though ln is just as accurate.

1) Taking log to both sides: log 2^y = log 256
2) The y moves to the front via a Law of Logarithms: y * log 2 = log 256
3) Divide both sides by log 2: y = log 256/log 2
4) Using your calculator: Answer is y = 8

Answer 4

This is a logarithm/exponential problem.

2^y =256
ln (2^y)=ln (256)
y ln 2 =ln (256)
y =ln (256)/ ln (2)
y =ln (256-2)
y =ln 254 That is as exact as it can get

Answer 5

2^y= 256
take the log of both sides.

y log(2) = log(256)

and divide.

y= (log(2)/log(256))
y= 8

Answer 6

.2^y=2^8
y=8