Question 372986
{{{10^(x+4)=5^(2x)}}} Start with the given equation.
 


{{{ln(10^(x+4))=ln(5^(2x))}}} Take the natural log of both sides.



{{{(x+4)ln(10)=2x*ln(5)}}} Pull down the exponents using the identity  {{{ln(x^y)=y*ln(x))}}}



{{{x*ln(10)+4*ln(10)=2x*ln(5)}}} Distribute



{{{4*ln(10)=2x*ln(5)-x*ln(10)}}} Subtract {{{x*ln(10)}}} from both sides.



{{{4*ln(10)=x(2*ln(5)-ln(10))}}} Factor out the GCF 'x' on the right side.



{{{(4*ln(10))/(2*ln(5)-ln(10))=x}}} Divide both sides by {{{2*ln(5)-ln(10)}}}.



{{{(4(ln(2)+ln(5)))/(2*ln(5)-(ln(2)+ln(5)))=x}}} Rewrite {{{ln(10)}}} as {{{ln(2*5)=ln(2)+ln(5)}}}



{{{(4ln(2)+4ln(5))/(2*ln(5)-ln(2)-ln(5))=x}}}  Distribute 




{{{(4ln(2)+4ln(5))/(ln(5)-ln(2))=x}}} Combine like terms.



So the real solution is {{{x=(4ln(2)+4ln(5))/(ln(5)-ln(2))}}}



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