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5^x+2  +2.5^x+1=875

5^x+1 .5+2.5^x+1=875

5^x+1. (5+2)=875

5^x+1 =875:7

5^x+1 =125

x+1 =3

x=2

5^x . 5^{x + 1} . 7 = 875

\(\Rightarrow\) 5^{2x + 1} = 875 : 7 = 125

\(\Rightarrow\) 5^{2x + 1} = 5³

\(\Rightarrow\) 2x + 1 = 3

\(\Rightarrow\) 2x = 2

\(\Rightarrow\) x = 1

5 + 3^{x + 1} = 86

\(\Rightarrow\) 3^{x + 1} = 81

\(\Rightarrow\) 3^{x + 1} = (\(\pm\)3)⁴

\(\Rightarrow\) x + 1 = \(\pm\)3

\(\Rightarrow\) x = 2, -4

2^x + 2^{x + 1} = 96

\(\Rightarrow\) 2^x + 2^x . 2 = 96

\(\Rightarrow\) 2^x . 3 = 96

\(\Rightarrow\) 2^x = 32

\(\Rightarrow\) 2^x = 2⁵

\(\Rightarrow\) x = 5

\(5^{x+1}+6.5^{x+1}=875\)

\(\Rightarrow5^{x+1}.\left(1+6\right)=875\)

\(\Rightarrow5^{x+1}.7=875\)

\(\Rightarrow5^{x+1}=875:7=125\)

\(\Rightarrow5^{x+1}=5^3\)

\(\Rightarrow x+1=3\)

\(\Rightarrow x=3-1=2\)

\(5^x.7.5^{x+1}=875\)

\(\Leftrightarrow5^x.5^{x+1}=125\)

\(\Leftrightarrow5^{2x+1}=5^3\)

\(\Leftrightarrow2x+1=3\)

\(\Leftrightarrow2x=2\Leftrightarrow x=1\)

\(5^{x+1}+6.5^{x+1}=875=>5^{x+1}\left(1+6\right)=875=>5^{x+1}=875:7=125=5^3\)

=>x+1=3

=>x=2

 5^x+1+6*5^x+1=875

=> 5^x+1.7 = 875

5^x+1=125 = 5³

x+1 = 3 

x = 2        

\(5^{x+1}+6.5^{x+1}=875\)

\(\Leftrightarrow7.5^{x+1}=875\)

\(\Leftrightarrow5^{x+1}=125=5^3\)

\(\Leftrightarrow x+1=3\)

\(\Leftrightarrow x=2\)

5^x . 7 . 5^x+1 = 875 

; 5^2x+1 = 125 = 5³

=> 2x + 1 = 3

=> 2x = 2

=> x = 1