Solve 5 2 x + 2 − 5 x + 2 + 6 = 0How...

klepkowy7c

klepkowy7c

Answered

2022-07-15

Solve 5 2 x + 2 5 x + 2 + 6 = 0
How do we solve 5 2 x + 2 5 x + 2 + 6 = 0? I know I have to use logarithms but I am not sure how to do it.

Answer & Explanation

Carassial3

Carassial3

Expert

2022-07-16Added 9 answers

Using a m x + n = a n ( a x ) m ,
we have
25 ( 5 x ) 2 25 ( 5 x ) + 6 = 0
which is a Quadratic Equation in 5 x
5 x = 25 ± 5 50 = 2 5 , 3 5
Taking logarithm,
x log 5 = log 2 log 5 , log 3 log 5
amacorrit80

amacorrit80

Expert

2022-07-17Added 1 answers

Let
5 x + 2 = y
25 × 5 x = y
5 x = y 25
5 2 x = y 2 625
5 2 x + 2 = y 2 25
The equation then, shall reduce to
y 2 25 y + 6 = 0
y 2 25 y + 150 = 0
This can be solved using quadratic equations.

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