Since 18 is a constant term, we can ignore it in terms of the inequality.
So, the final inequality is:
3(2^x)^2 - 5(2^x)^(log2(6)) < 0
This inequality can be further simplified by using some properties of logarithms, but it may not be possible to find an exact solution without using numerical methods.
To solve the inequality, we can rewrite it as:
3(2^x)^2 + 2(3^x)^2 - 5(23)^x < 0
Let's make a substitution:
Let y = (2^x)^2
Now the inequality becomes:
3y + 23^(2log3(y)) - 5y^(log3(6)) < 0
Simplify the inequality further:
3y + 23^(2(xlog2(2))) - 5*y^(log3(6)) < 0
3y + 18 - 5*y^(log3(6)) < 0
Rewrite the inequality back in terms of x:
3(2^x)^2 + 18 - 5(2^x)^(log2(6)) < 0
Since 18 is a constant term, we can ignore it in terms of the inequality.
So, the final inequality is:
3(2^x)^2 - 5(2^x)^(log2(6)) < 0
This inequality can be further simplified by using some properties of logarithms, but it may not be possible to find an exact solution without using numerical methods.