Find the solution \(\displaystyle{{\log}_{{3}}{\left({2}{x}\right)}}+{{\log}_{{3}}{\left({2}{x}+{3}\right)}}-{{\log}_{{32}}=}{2}\)

Devin Dougherty

Devin Dougherty

Answered question

2022-04-08

Find the solution
log3(2x)+log3(2x+3)log32=2

Answer & Explanation

Kendall Wilkinson

Kendall Wilkinson

Beginner2022-04-09Added 17 answers

log3(2x)+log3(2x+3)log32=2
log3(2x(2x+3))log32=2
log3(2x(2x+3)2)=2
log3(x(2x+3))=2
x(2x+3)=32=9
2x2+3x9=0
2x2+6x3x9=0
2x(x+3)3(x+3)=0
(2x3)(x+3)=0
x=3, x=32

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