4^x= 64 solve exponential equation?

Answer 1

2 ways:

4^x= 64
log_base 4 (64) = x
log 64 / log 4 = x
x = 3

or you can do it this way:
4^x= 64
4^x = 4^3 <-- Since they have the same base now, 4's cancel, leaving only the exponents.
x = 3

Answer 2

X= 3, since 4^3=64.

Answer 3

4^x=64
which means how many 4s times together (x) makes 64
so 1. 64/4=16
2. 16/4=4

so 4x4x4=64

therefore x=3

Answer 4

Taking log to base 4 (some of the other answers) is kind of cheating - since you're starting with the answer.

Rules of logs work in any base. I'll pick base-2.

4^x = 64
x=log2(64)/log2(4)
x=6/2
x=3

Now I'll use base-10 (available on most scientific calculators, and even Windows PCs)
x=log10(64)/log10(4)
x=1.80617997398/0.60205999133
x=3

This even works in base e (natural log - ln button on a calculator)
x=ln(64)/ln(4)
x=4.15888308336/1.38629436112
x=3

Answer 5

4^x = 64
Take log base 4 of both sides
x log 4 = log 64
x X 1 = 3
x = 3

Answer 6

log (a million/sixteen) = (4*x - 3)*log sixty 4 - log sixteen = (4*x - 3)*log sixty 4 4*x - 3 = -(log sixteen/log sixty 4) = - log 2^4 / log 2^6 = - 4*log 2/ 6*log 2 = - 2/3 4*x - 3 = -2/3 4*x = 9/3 - 2/3 = 7/3 x = 7/12 <<<

Answer 7

4x4x4= 64

therefore x = 3

Answer 8

4^x= 64 .............4^x = 4^3............x =3

Answer 9

4x=64
divide 4 on both sides
x=16