Use the rules of exponents and logarithms to solve the equation.
[tex]\bf{\dfrac{1}{16}\times4^{x}=64 }[/tex]
Multiply both sides by 16.
[tex]\bf{4^{x}=1024 }[/tex]
Take the logarithm of the two sides of the equation.
[tex]\bf{log(4^{x} )=log(1024) }[/tex]
The logarithm of a number raised to a power is the power multiplied by the logarithm of the number.
[tex]\bf{x \ log(4)=log(1024) }[/tex]
Divide the two sides by log(4).
[tex]\bf{x=\dfrac{log(1024)}{log(4)} }[/tex]
By the base change formula [tex]\bf{\frac{log(a)}{log(b)}=log_{b}(a). }[/tex]
[tex]\bf{x=log_{4}(1024) }[/tex]
x = 5 ====> Answer
