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Mathematics
OpenStudy (anonymous):

Solve the inequality. 8^x<512

OpenStudy (netlopes1):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

yes but i would need that to get 2^9

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

ok so it has to be the lowest common multiple?

OpenStudy (anonymous):

he use the lowest common base for the exponential.

OpenStudy (anonymous):

used**

OpenStudy (anonymous):

oh ok i think i get it now

OpenStudy (anonymous):

and if the bases are equal, the exponents MUST be equal: |dw:1338075296879:dw|

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