I have to solve this equation, 2^x*6^(x−2)=5^(2x)*7^(1−x). Now, I started by taking logs on both sides which gives me this funny looking equation xlog2+(x−2)log(2*3)=2xlog(10/2)+(1−x)log7 I have been stuck on this step for a while now and can't see how I can go further from here. Is there a way out?

Elsa Brewer

Elsa Brewer

Answered question

2022-07-23

Solve 2 x 6 x 2 = 5 2 x 7 1 x
I have to solve this equation, 2 x 6 x 2 = 5 2 x 7 1 x . Now, I started by taking logs on both sides which gives me this funny looking equation
x log 2 + ( x 2 ) log ( 2 3 ) = 2 x log ( 10 2 ) + ( 1 x ) log 7
I have been stuck on this step for a while now and can't see how I can go further from here. Is there a way out?

Answer & Explanation

sweetwisdomgw

sweetwisdomgw

Beginner2022-07-24Added 20 answers

It's
x ln 2 + ( x 2 ) ln 6 = 2 x ln 5 + ( 1 x ) ln 7 ,
which gives
x = 2 ln 6 + ln 7 ln 2 + ln 6 2 ln 5 + ln 7
or
x = log 84 25 252
pliwraih

pliwraih

Beginner2022-07-25Added 4 answers

2 x × 6 x 6 2 = ( 5 2 ) x × 7 1 7 x
2 x × 6 x × 7 x ( 5 2 ) x = 7 1 × 6 2
( 2 × 6 × 7 25 ) x = 7 1 × 6 2
so
x = ln ( 7 1 × 6 2 ) ln ( 2 × 6 × 7 25 )

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