Question

Solve 5^(3x + 1) = 25^(x + 1)

a. x = 4
b. x = -2
c. x = 1
d. x = 0

and could you explain how you got it, so I can understand.

Answer 1

x = 1

Answer 2

\[5^{3x+1}=25^{x+1}\]
=
\[5^{3x+1}=5^{2(x+1)}\]
=\[equating\ powers\]
\[3x+1=2x+2\]
\[x=1\]

Answer 3

this is the whole procedure

Answer 4

\[5^(3x+1) = 25^(x+1) = 5^{2\times(x+1)} \]
as common base on both sides
so,\[3x + 1 = 2(x+1)\]
solve for x

Answer 5

\[5^{3x+1}=25^{x+1}, 5^{3x+1}=5^{2(x+1)}, 5^{3x+1}=5^{2x+2}\]
\[3x+1=2x+2\]
You can substitute and bring 2x on the other side and take 1 on the other side, which leads to this (Also, when you substitute, positive values turn negative, e.g 2x becomes -2x when brought on other side):
\[3x-2x=-1+2\]
\[\therefore x=1\]