Question

log {2^(x+2) - 4^(x) } of base 1/3 >= (-2)

can any one tell the method to solve

Answer 1

heyy its base is 10 na????

Answer 2

\(\Huge \log_{\frac 13} 2^{(x+2)} - 4^x \ge -2\)

^right?

Answer 3

yup the format is the one lgbasallote typed

Answer 4

well you could get rid of log by changing to exponential form
\[2^{x+2} -4^{x} \ge (1/3)^{-2}\]
simplify so you have same base
\[4*2^{x} -2^{2x} \ge 9\]
let u = 2^x
it becomes a quadratic
\[u^{2}-4u+9 \le 0\]
use quadratic formula
...

Answer 5

finally once you have the 2 roots , u1 and u2
\[u_{1} \le 2^{x} \le u_{2}\]