I am completey stuck on this problem Please show each step w

I am completey stuck on this problem. Please show each step when solving

thank you

Solve the exponential equation 8^logX-3-4,6.2^logx + 8 = 0.

8^logx - 4.3^logx -6.2^logx +8 =0

express each tem in terms of 2^logx

2^(3logx) - 4.2^(2logx) -6.2^logx +8 =0

(2^logx)^3 - 4(2^logx)^2 -6.(2^logx)^1 +8 =0

Let 2^logx = y

(2^logx)^3 -(2^logx)^2 -6.(2^logx)^ +8 =0

y^3 -4y^2 -6y +8 =0

Now find the roots of the cubic equation using cubic root formula

y =0.90 ,- 1.8 , 4.9

Neglect -ve values as exponential function cannot be -ve

So, 2^logx = 0.9 and 2^logx =4.9

Taking log of both sides:logx* log2 = log0.9

logx = log0.9/log2 ----> x= 10^l(og0.9/log2 )

x= 10^(log0.9/log2 ) =0.707

Similarly : 2^logx =4.9

Taking log of both sides: logx*log2 = log4.9

x = 10^(log4.9/log2) =195