Question

Tìm x:

a) 3 . 5^{x - 3} + 5² = 10²

b) (11 + 4^{x - 5}) : 3² = 3

c) 53 - 11 . 2^{2x - 6} = 3⁵ : 27

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Answer 1

a: \(\Leftrightarrow3\cdot5^{x-3}=100-25=75\)

=>5^x-3=5²

=>x-3=2

=>x=5

b: \(\Leftrightarrow11+4^{x-5}=27\)

=>4^x-5=16

=>x-5=2

=>x=7

c: \(\Leftrightarrow11\cdot2^{2x-6}=53-9=44\)

=>2x-6=2

=>2x=8

=>x=4

Answer 2

a, \(3.5^{x-3}+5^2=10^2\)

\(\Leftrightarrow3.5^{x-3}+25=100\)

\(\Leftrightarrow3.5^{x-3}=100-25\)

\(\Leftrightarrow3.5^{x-3}=75\)

\(\Leftrightarrow5^{x-3}=25\)

\(\Leftrightarrow5^{x-3}=5^2\)

\(\Leftrightarrow x-3=2\)

\(\Leftrightarrow x=5\)

b, \(\left(11+4^{x-5}\right):3^2=3\)

\(\Leftrightarrow\left(11+4^{x-5}\right):9=3\)

\(\Leftrightarrow11+4^{x-5}=27\)

\(\Leftrightarrow4^{x-5}=16\)

\(\Leftrightarrow4^{x-5}=4^2\)

\(\Leftrightarrow x-5=2\)

\(\Leftrightarrow x=7\)

c, \(53-11.2^{2x-6}=3^5:27\)

\(\Leftrightarrow53-11.2^{2x-6}=243:27\)

\(\Leftrightarrow53-11.2^{2x-6}=9\)

\(\Leftrightarrow-11.2^{2x-6}=-44\)

\(\Leftrightarrow2^{2x-6}=4\)

\(\Leftrightarrow2^{2x-6}=2^2\)

\(\Leftrightarrow2x-6=2\)

\(\Leftrightarrow2x=8\)

\(\Leftrightarrow x=4\)