Math

Question Solve the equation 1162x+1=16\frac{1}{16^{2x+1}} = 16 for xx.

Studdy Solution

STEP 1

Assumptions
1. The equation is 1162x+1=16\frac{1}{16^{2 x+1}}=16
2. We are solving for xx

STEP 2

First, we can rewrite the equation to make it easier to solve. We can write 1616 as 16116^{1} and 162x+116^{2x+1} as 16(2x+1)16^{-(2x+1)}.
16(2x+1)=16116^{-(2x+1)} = 16^{1}

STEP 3

Since the bases are the same, we can set the exponents equal to each other.
(2x+1)=1-(2x+1) = 1

STEP 4

Solve the equation for xx by first adding (2x+1)(2x+1) to both sides to get rid of the negative sign.
2x+1=12x+1 = -1

STEP 5

Subtract 11 from both sides to isolate 2x2x on the left side of the equation.
2x=112x = -1 - 1

STEP 6

Calculate the right side of the equation.
2x=22x = -2

STEP 7

Finally, divide both sides by 22 to solve for xx.
x=22x = \frac{-2}{2}

STEP 8

Calculate the value of xx.
x=1x = -1
So, x=1x = -1 is the solution to the equation 1162x+1=16\frac{1}{16^{2 x+1}}=16.

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