Adding Logarithms Studying for my midterm. Solve the following algebraically: log

Avah Knapp

Avah Knapp

Answered question

2022-05-20

Adding Logarithms
Studying for my midterm.
Solve the following algebraically:
log 2 x + log 2 ( x + 4 ) = 5
So I know that log b ( m n ) = log b ( n ) + log b ( m ) therefore:
5 = log 2 ( x ( x + 4 ) )
or
5 = log 2 ( x 2 + 4 x )
5 = 2 x 2 + 4 x
Now I don't know how to solve for x at this point. I'm stuck. Please let me know if I've done anything wrong in my calculations. The answer key says that x = 4

Answer & Explanation

coquinarq1

coquinarq1

Beginner2022-05-21Added 14 answers

You rewrote the expression incorrectly. It should be x 2 + 4 x = 2 5
Camille Flynn

Camille Flynn

Beginner2022-05-22Added 6 answers

You just used the rules of logarithms incorrectly at your last step.
It should be x 2 + 4 x = 2 5 - remember that a = log b c a = log b c means b a = c

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