How to solve complicated logarithmic equations?
Hi, can someone please help me with question 10 e and f? Thanks!
Hi, can someone please help me with question 10 e and f? Thanks!
2 Answers
Explanation:
These questions are tricky because you have a constant in between all of those logs. To get around this, turn them into logs so in this case:
Once you've done this, youcan use your other log laws to solve the equations:
Do the same to the other side and you'll get:
You can now remove the logs:
The second question will become:
Expand and collect to leave
Explanation:
Here's how I would do question
Put all the logarithms to one side.
1=log10(2x+1)−2log10(x+1)+log10(5x+8)
Use
1=log10((2x+1)(5x+8)(x+1)2)
1=log10(10x2+21x+8(x+1)2)
Convert to exponential form. If
101=10x2+21x+8x+1
10(x+1)2=10x2+21x+8
10x2+20x+10=10x2+21x+8
10−8=21x−20x
x=2
Hopefully this helps!