243\cdot7^{x-1}=343\cdot3^{x+1}\\

FobelloE

FobelloE

Answered question

2021-11-05

243\cdot7^{x-1}=343\cdot3^{x+1}\

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-11-06Added 104 answers

Step 1
To solve any exponential equation, logarithms are taken on both sides of the equation. Once the logarithms have the same base on both sides of the equation, they are eliminated and the arguements are then further simplified.
Step 2
Now, to solve the equation 2437x1=3433x+1 logarithms are applied on both sides of the equation. When they are applied, it is observed that the arguements are multiplied. Therefore the logarithmic property log(ab)=log(a)+log(b) can be used to simplify the equation. It is also known that 243=34and 343=73.Some other logarithmic properties that can be used here is log(xn)=nlog(x) and log(ab)=log(a)log(b). Using these properties the value of x can be found.
2437x1=3433x+1
log(243·7x1)=log(3433x+1)
log(243)+log(7x1)=log(343)+log(3x+1)
log(7x1)log(3x+1)=log(343)log(243)
(x1)log(7)(x+1)log(3)=log(73)log(34)
xlog(7)log(7)xlog(3)log(3)=3log(7)4log(3)
x(log(7)log(3))=3log(7)4log(3)+log(7)+log(3)
x=4log(7)3log(3)log(7)log(3)

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