Question

a) [tex] 25^{2x+3} = 125^{6}[/ tex]
b)$4^{3x-2}= 2^{14}$
c)$8^{2x+1} = 2^{21}$

Answer 1

   
$a) \\ 25^{2x+3}=125^6 \\ (5^2)^{2x+3}=(5^3)^6 \\ 5^{2(2x+3)}=5^{3\;\cdot\;6} \\ 2(2x+3)=3 \cdot 6 \\ 4x+6=18 \\ 4x=18-6 \\ 4x=12 \\ x= \frac{12}{4} =\boxed{3}$

$b) \\ 4^{3x-2}=2^{14} \\ (2^2)^{3x-2}=2^{14} \\ 2^{}=2^{14} \\ 2(3x-2)=14 \\ 6x-4=14 \\ 6x=14+4 \\ 6x=18 \\ x= \frac{18}{6} =\boxed{3}$

$c) \\ 8^{2x+1}=2^{21} \\ (2^3)^{2x+1}=2^{21} \\ 2^{3(2x+1)}=2^{21} \\ 3(2x+1)=21 \\ 6x+3=21 \\ 6x=21-3 \\ 6x=18 \\ x= \frac{18}{6} =\boxed{3}$

Answer 2

  a.
 $25^{2x+3} =125^{6}$
$5^{2(2x+3)} = 5^{(3)(6)}$
2(2x+3)=3×6  se simplifica cu 2 ⇒ 2x+3=9  ⇒ 2x=9-3⇒ 2x=6⇒x=6:2=3
x=3

b.  [tex] 4^{3x-2} = 2^{14} [/tex]
$2^{2(3x-2)} = 2^{14}$
2(3x-2)=14
6x-4=14⇒  6x=14+4⇒  6x=18⇒ x=18:6⇒ x=3
x=3

c. $8^{2x+1)} = 2^{21}$
$2^{3(2x+1)} = 2^{21}$
3(2x+1)=21⇒  6x+3=21⇒  6x=21-3⇒  6x=18⇒  x=18:6⇒x=3
x=3