A Simple Logarithm Question Solve for x: log_2(2x+8)=3

Lisantiom

Lisantiom

Answered question

2022-10-07

A Simple Logarithm Question
Solve for x: log 2 ( 2 x + 8 ) = 3
Correct Solution:
2 x + 8 = 2 3
2 x + 8 = 8
2 x = 0
x = 0
Why doesn't this work:
log 2 ( 2 x + 8 ) = 3
Expand:
log 2 ( 2 x ) + log 2 8 = 3
log 2 ( 2 x ) + 3 = 3
log 2 ( 2 x ) = 0
2 x = 2 0
2 x = 1
x = 1 / 2
Thank you

Answer & Explanation

Frederick Espinoza

Frederick Espinoza

Beginner2022-10-08Added 7 answers

Note that
log 2 ( 2 x + 8 ) log 2 ( 2 x ) + log 2 ( 8 ) .
We have log 2 ( 2 x ) + log 2 ( 8 ) = log 2 ( 2 x × 8 )
Ratuiszt

Ratuiszt

Beginner2022-10-09Added 1 answers

One more way: to make yr life easier use the property of yhe logsrithm:
log a b = ln b ln a
wher3 ln is a natural log. After a bit of algebra exponentiate both sides.

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