Question

If 16 to the power of x equals 1/64 find the value of x

Answer 1

`\sf x = (-3)/(2)`

Explanation:

Exponents:

Prime factorize 16 and 64 and write in exponent form.

`\sf \boxed{\bf (1)/(a^m)=a^(-m)}\\\\\\\boxed{\bf (a^m)^n =a^(m*n)}`

`\sf 16^x = (1)/(64)\\\\ (4^2)^x= 64^(-1)\\\\ (4^2)^x = (4^3)^(-1)\\\\ 4^(2x)=4^(-3)`

As bases are same, compare the powers.

2x = -3

`\sf x = (-3)/(2)`