Question

16^x=64
solve the equation for x. if necessary round your answer to two decimal places.

Answer 1

i got 3/2. but it doesnt work.

Answer 2

\[16^{x}=64\]

Answer 3

keep in mind that \(\bf 16^x= 64 \\
16 = 2^4, 64 = 2^6\\
16^x= 64 \implies 2^{4x} = 2^6\)

Answer 4

ok

Answer 5

start by rewriting both sides of the equation with the same base... base 4

\[16^x = (4^2)^x = 4^{2x}\]

and

\[64 = 4^3\]


so you are now solving

\[4^{2x} = 4^3\]

so just equate the powers and solve for x

Answer 6

im lost

Answer 7

\[4^{2x} is 1048576\]

Answer 8

\[4^{3} is 64\]

Answer 9

so x = 3/2 which is the correct and

so go back to the initial question and substitute

\[16^{\frac{3}{2}} = 64\]

Answer 10

thanks.