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Solve for x if 1/8=16^x.

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swavers | Student, Grade 11 | eNoter

Posted January 13, 2011 at 9:44 AM via web

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Solve for x if 1/8=16^x.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 13, 2011 at 10:51 AM (Answer #1)

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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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neela | High School Teacher | Valedictorian

Posted January 13, 2011 at 10:54 AM (Answer #2)

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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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