Question: Could someone please check my work Show that 2 = 3x for some a E (0, 1) . Since 27 = 3x , then 2*

Could someone please check my work Show that 2" = 3x

Could someone please check my work

Show that 2" = 3x for some a E (0, 1) . Since 27 = 3x , then 2* - 3x = 0 , so let f(2) = 23 - 3x = 0 NOT Sure I Can say This by Theorem 4.21. Suppose In -> c . Then by Theorem 5. 1.13, ggen show lim f(*n) = lim [2*m - 3x] = 2 limon] / 3[ lim x] by Theorem 4.2.1 = 20 - 3c = f(c) Thus, by Theorem 5.2.2, f is continuous at c f(0) = 20 - 3(0) = 1>0 GMT Laws 20 03 210 $.2.1 THEOREM Suppose that (Sn) and (tn) are convergent sequences with lim s, = f(1) = 21 - 3(1) = -1

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