Simplfy a^logaX^3 and use it to find the maximum possible value of 8(27^log6X)+27(8^log6X)-X^3, given that x is a real number.

a^logaX^3 = x^3,

Let y = 8(27^log_6 X)+27(8^log_6 X)-X^3

y = 8(27^log_6 X)+27(8^log_6 X) - 6^(log_6 x^3)

= 216 when x = 6,

THUS, global maximum is when x = 6.

i plot it first and by observation, the logarithmic function gets a maximum @ about x = 6. So i guess, max when x = 6.

ok