a)
x : $7^{10}$ = 7
⇔ x = 7 x $7^{10}$
⇔ x = $7^{11}$
b)
x : 5 = $5^{12}$
⇔ x = $5^{12}$ x 5
⇔ x = $5^{13}$
c)
x : $4^{3}$ = $4^{5}$
⇔ x = $4^{5}$ x $4^{3}$
⇔ x = $4^{8}$
d)
$2^{3}$ x X = 32
⇔ x = $2^{5}$ : $2^{3}$
⇔ x = $2^{2}$
e)
$3^{x}$ = 81
⇔ x = $3^{4}$ ( vì 3 x 3 x 3 x 3 = 81 ⇒ $3^{4}$ = 81 )
f)
$4^{x - 1}$ = 16
⇔ x = 3 ( vì $4^{2}$ = 16; x - 1 = 2 ⇒ x = 3 )
g)
$\frac{50}{5^{x}}$ = 2
⇔ x = 5 ( vì $\frac{50}{25}$ = 2; 25 = $5^{5}$ )
h)
$3^{3x+1}$ = $3^{10}$
⇔ x = 3 ( vì 3x + 1 = 10; 3x = 9 ⇒ x = 3 )
so sánh : $2^{30 }$ và $3^{20}$
$2^{30}$ = $2^{3x10}$ = ($2^{3}$ )$^{10}$ = $8^{10}$
$3^{20}$ = $3^{2x10}$ = ($3^{2}$ )$^{10}$ = $9^{10}$
⇒ $8^{10}$ < $9^{10}$ nên $2^{30}$ < $3^{20}$
