Solve for x if 1/8=16^x.
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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
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The equation 1/8=16^x has to be solved for x.
8 can be written as a power of 2, `8 = 2^3` . Similarly, `16 = 2^4` . The given equation can be written as:
`1/2^3 = (2^4)^x`
Use the relation `a^-1 = 1/a` , `(a^b)^c = (a^c)^b`
`2^-3 = (2^x)^4`
`2^(-3/4) = 2^x`
As the base is the same the exponent can be equated to solve for x.
x = -3/4
The solution of the equation is x = -3/4
To solve for x: 1/8 = 16^x.
LHS = 1/8 = 1/2^# = 1/2^(-3).
RHS = 16^x = (2^4)^x = 2^4x.
Therefore the given equation is rewritten as:
2^(-3) = 2^4x.
Or 2^4x = 2^(-3).
The bases are same. So we equate the exponents:
4x = -3.
4x/4 = -3/4
x = -0.75
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