Question

Solve the inequality.
8^x<512

Answer 1

\[8^{x}<512\]\[\rightarrow 2^{3x}<2^{9}\rightarrow3x<9\rightarrow x<3\]

Answer 2

how did u come across that answer for 512 how did u find that?

Answer 3

he wrote both sides of the inequality as exponential with the same base...

Answer 4

yes but how did he know that 512 was divisble by 2?

Answer 5

512 is even, but that's not the point...

Answer 6

yes but i would need that to get 2^9

Answer 7

2^9 = 2*2*2*2*2*2*2*2*2 = 512

Answer 8

2^3 = 2*2*2 = 8
this is how he was able to change that left side to 2^(3x)

Answer 9

ok so it has to be the lowest common multiple?

Answer 10

he use the lowest common base for the exponential.

Answer 11

used**

Answer 12

oh ok i think i get it now

Answer 13

and if the bases are equal, the exponents MUST be equal: