Answer:
x=335
Step-by-step explanation:
The given expression is
[tex]8^{2x+3}+8^{2x+1}-8^{2x}=519*2^{2010}[/tex]
Apply the reverse of the product rule: [tex]a^{m+n}=a^m\times a^n[/tex]
[tex]8^{2x}\times 8^3+8^{2x}\times 8^1-8^{2x}=519*2^{2010}[/tex]
Factor on the left
[tex](8^3+ 8^1-1})8^{2x}=519*2^{2010}[/tex]
Evaluate
[tex](512+ 8-1})8^{2x}=519*2^{2010}[/tex]
Simplify:
[tex]519*8^{2x}=519*2^{2010}[/tex]
Divide through by 519
[tex]8^{2x}=2^{2010}[/tex]
Write the the LHS as a power of 2.
[tex]2^{3*2x}=2^{2010}[/tex]
[tex]2^{6x}=2^{2010}[/tex]
Equate the exponent
[tex]6x=2010[/tex]
Divide by 6
x=335
