Question 596631
{{{ln(2^(4x-1))=ln(8^(x+5))+log(2, (16^(1-2x))))}}}
You have done a lot of the work already. Your equation:
{{{ln(2^(x-16))=4-8x}}}
is correct. The next step is to use a property of logarithms, {{{log(a, (p^q)) = q*log(a, (p))}}}, to move the exponent of the argument out in front:
{{{(x-16)ln(2)=4-8x}}}<br>
Multiplying out the left side we get:
{{{x*ln(2)-16ln(2)=4-8x}}}<br>
Next we gather all the terms with on in them on one side of the equation and the other terms on the other side. Adding 8x and 16ln(2) to each side we get:
{{{x*ln(2) + 8x = 16ln(2) + 4}}}<br>
Next we factor out x on the left side:
{{{x(ln(2) + 8) = 16ln(2) + 4}}}
And last we divide both sides by (ln(2) + 8):
{{{x = (16ln(2) + 4)/(ln(2) + 8)}}}<br>
And since the fraction on the right will not simplify, we are finished!