What is X in this equation 4^x=16384, and how possibly could I find it myself?

Answer 1

To find x in 4^x = 16384, you need to use logs. Since x is in the exponent, the only way to free it from the exponent is to use logs.

We can log both sides:

log (4^x) = log (16384)

Using log properties, we can bring the x out front, to make it:

x * log(4) = log(16384)

To isolate x, we can divide both sides by log(4):

x = log(16384)/log(4)

When you plug this into your calculator (remember to close parentheses), you get 7. x = 7. I hope this helps!

Answer 2

If you are asked to answer this question without the aid of a calculator on a test, you will have some trust that 16384 is 4 raise to a whole number. So to find it on your own you would just keep finding the powers of 4 (ie 4, 16, 64, .... until you got to 16384). It's a bit tedious granted, but most teachers won't expect you to do this large of a number on a test without a calculator.