Solve for x

Question

Solve for x:

 

8^2-x=16^2x+1

Answer 1

Can you rewrite this problem so that the bases are the same on each side of the equals sign?

 

We know that 8 = 2 x 2 x 2 = 2³

 

Furthermore, 16 = 2 x 2 x 2 x 2 = 2⁴

 

The problem can be rewritten as

 

(2³)^2-x = (2⁴)^{2x + 1}

 

(2)^{6 - 3x} = (2)^{8x + 4}

 

When the bases are the same, we can equate the exponents and solve for x.

 

Can you solve the equation 6 - 3x = 8x + 4 ?

Answer 2

You can also solve this using logarithms:

 

8^2-x = 16^2x+1

 

log(8^2-x) = log(16^2x+1)

 

(2 - x)log8 = (2x + 1)log16

 

log8 = log(2³) = 3log2

 

log16 = log(2⁴) = 4log2

 

Therefore,

 

(2 - x)(3log2) = (2x + 1)(4log2)

 

(2 - x)(3) = (2x + 1)(4)

 

6 - 3x = 8x + 4

 

Now do simple algebra to complete the solution.

Answer 3

8^2-x = 16^2x+1

(2³)^2-x = (2⁴)^2x+1

2^6-3x = 2^8x+1

 

Can you solve for x?