Question

8^(2x+3)+8^(2×+1)-8^2×=519*2^2010
x=?

Answer 1

x=335

Explanation:

The given expression is

`8^(2x+3)+8^(2x+1)-8^(2x)=519*2^(2010)`

Apply the reverse of the product rule:
`a^(m+n)=a^m* a^n`

`8^(2x)* 8^3+8^(2x)* 8^1-8^(2x)=519*2^(2010)`

Factor on the left

`(8^3+ 8^1-1})8^(2x)=519*2^(2010)`

Evaluate

`(512+ 8-1})8^(2x)=519*2^(2010)`

Simplify:

`519*8^(2x)=519*2^(2010)`

Divide through by 519

`8^(2x)=2^(2010)`

Write the the LHS as a power of 2.

`2^(3*2x)=2^(2010)`

`2^(6x)=2^(2010)`

Equate the exponent

`6x=2010`

Divide by 6

x=335