SOLUTION: Solve x in the following exponential equation {{{ 2^(2x) * 4^(4x+8) =64 }}}

Algebra ->  Exponents -> SOLUTION: Solve x in the following exponential equation {{{ 2^(2x) * 4^(4x+8) =64 }}}      Log On


   

Question 641760: Solve x in the following exponential equation +2%5E%282x%29+%2A+4%5E%284x%2B8%29+=64+
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+2%5E%282x%29+%2A+4%5E%284x%2B8%29+=64+
+2%5E%282x%29+%2A+2%5E2%284x%2B8%29+=2%5E6+
+2%5E%282x%29+%2A+2%5E%288x%2B16%29+=2%5E6+
+2%5E%282x%2B8x%2B16%29+=2%5E6+
+2%5E%2810x%2B16%29+=2%5E6+
if base equal, exponents are equal too

+10x%2B16=6+.
+10x=6-16+
+10x=-10+
+x=-1+

check:
+2%5E%282%28-1%29%29+%2A+4%5E%284%28-1%29%2B8%29+=64+
+2%5E%28-2%29+%2A+4%5E%28-4%2B8%29+=64+

+%281%2F2%5E2%29+%2A+4%5E4+=64+

+%281%2F4%29+%2A+256+=64+


++256%2F4+=64+


+64+=64+