# Solve for x if 1/8=16^x.

Given the equation:\

1/8 = 16^x

First we will simplify 8 and 16 as powers of the prime number 2.

We know that:

8 = 2*2*2 = 2^3

16 = 4*4 = 2*2*2*2 = 2^4

Now we will rewrite into the given equation:

==> 1/(2^3) = (2^4)^x

Now we will...

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Given the equation:\

1/8 = 16^x

First we will simplify 8 and 16 as powers of the prime number 2.

We know that:

8 = 2*2*2 = 2^3

16 = 4*4 = 2*2*2*2 = 2^4

Now we will rewrite into the given equation:

==> 1/(2^3) = (2^4)^x

Now we will use the exponent properties to solve.

We know that:

1/a^x = a^-x Therefore, 1/2^3 = 2^-3

Also, we know that:

(x^a)^b = x^(ab). Therefore, 2^4^x = 2^(4x)

Now we will substitute into the equation.

==> 2^-3 = 2^4x

Now since the bases are equal, then the powers are equal too.

==> -3 = 4x

We will divide by 4 to solve for x.

==> x = -3/4

Approved by eNotes Editorial Team