\(ln2^{4x-1}=ln8^{x+5}+log_2 16^{1-2x}\)
the right handside \(log_2 16^{1-2x}\) we can make the power (1-2x) next to the log so we could solve for 2^y=16 which will be 4
\((1-2x)*log_2 16\)
\(log_2 16 = 4\)
4*(1-2x) + \(ln8^{x+5}\)=\(ln2^{4x-1}\)
4-8x+(x+5)*\(ln8\)=(4x-1)*\(ln2\)
\(\frac{4-8x+(x+5)*ln8}{4x-1}=ln2\)
Expressed in terms of ln2
Further simplify could be done by using calculator
ln8=2.07944154
4-8x+(x+5)*2.07944154
4-8x+2.079444154x+10.3972077
4-5.920x+10.3972077
14.3972077-5.920x/4x-1 =ln2
ln2=0.693147
14.4-5.9x=(4x-1)*0.693147
Rest is just algebra and indeed you will find that
indeed you will find x=1.73589087 approx: 1.74
Which works.
I don't think the question wants the x value so just expressed it in ln2