Solve the exponential equation 32^(x+3)=4^(3x+5) for x {-4} {5} {} {-1}

abelynybco

abelynybco

Answered question

2022-10-08

Solve the exponential equation 32 x + 3 = 4 3 x + 5 for x
{-4}
{5}
{}
{-1}

Answer & Explanation

Mckenna Friedman

Mckenna Friedman

Beginner2022-10-09Added 10 answers

Given enponential equation
32 x + 3 = 4 3 x + 5
we have to solve it for x. Therefore,
32 x + 3 = 4 3 x + 5
on taking log 2 (Base 2) both sides, we get,
( x + 3 ) log 2 32 = ( 3 x + 5 ) log 2 4
( x + 3 ) log 2 ( 2 ) 5 = ( 3 x + 5 ) log 2 ( 2 ) 2
5 ( x + 3 ) log 2 2 = 2 ( 3 x + 5 ) log 2 2
Since log 2 2 = 1, so
5 ( x + 3 ) = 2 ( 3 x + 5 )
5 x + 15 = 6 x + 10
6 x 5 x = 15 10
6 x 5 x = 15 10
x = 5
Thus,
x=5 Answer

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