Question 1198055
 Solve the indicial linear equation 5√8^2x=128^x X 64 
:
{{{5sqrt(8^(2x))=128^x * 64}}}
 rewrite this using exponents
{{{5*(8^(2x))^(1/2) = 128^x * 64}}}
{{{5*(8^(2x*(1/2))) = 128^x * 64}}}
cancel the 2
{{{5*(8^x) = 128^x * 64}}}
put what we can into base 2
{{{5*(2^(3x)) = 2^(7x) * 64}}}
{{{5/64 = 2^(7x-3x)}}}
{{{5/64 = 2^(4x)}}}
write it
{{{2^(4x) = 5/64}}}
 4x*ln(2) = ln(5/64)
4x = {{{ln(5/64)/ln(2)}}}
4x = -3.678
x = {{{(-3.678)/4}}}
x = -.9195