Question

5 mũ x .5 mũ x +1 . 7 =875

5 + 3 mũ x +1=86

2 mũ x +2 mũ x +1 = 96

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

5 + 3^{x + 1} = 86

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

\(\Rightarrow\) 3^{x + 1} = 3⁴

\(\Rightarrow\) x + 1 = 4

\(\Rightarrow\) x = 3