logarithms equations, Hello I have following problem: solve equation log &#x2061;<!-- ⁡ -->

Llubanipo

Llubanipo

Answered question

2022-06-24

logarithms equations,
Hello I have following problem: solve equation log ( x 5 ) 2 + log ( x + 6 ) 2 = 2and I rewrited this equation as
2 log ( x 5 ) + 2 log ( x + 6 ) = log 100 2 ( log ( x 5 ) ( x + 6 ) ) = log 100 log x 2 + x 30 = log 10 x 2 + x 40 = 0
and I solved this equation, but I obtained only two solutions and there should be four, so I wonder if it is necessary to create log ( x 5 ) 2 ( x + 6 ) 2 = log 100 or is a simplier way.

Answer & Explanation

Mateo Barajas

Mateo Barajas

Beginner2022-06-25Added 13 answers

log ( x 5 ) 2 + log ( x + 6 ) 2 = 2
log ( ( x 5 ) ( x + 6 ) ) 2 = 2
( ( x 5 ) ( x + 6 ) ) 2 = 10 2 = 100
( x 5 ) ( x + 6 ) = ± 10
Solve from here
Devin Anderson

Devin Anderson

Beginner2022-06-26Added 6 answers

As the logarithm term contains squares, we can allow x 5 , x + 6 to be negative
In fact, log b 2 = 2 log | b | for real b
As log A + log B = log ( A B ) ,
log 10 { ( x 5 ) ( x + 6 ) } 2 = 2
{ ( x 5 ) ( x + 6 ) } 2 = 10 2 = 100
( x 5 ) ( x + 6 ) = ± 10

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