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 = log_10(2x + 1) - 2log_10(x + 1) + log_10(5x + 8)#
Use
#1 = log_10 (((2x + 1)(5x+ 8))/(x + 1)^2)#
#1 = log_10( (10x^2 + 21x + 8)/(x + 1)^2)#
Convert to exponential form. If
#10^1 = (10x^2 + 21x + 8)/(x + 1)#
#10(x + 1)^2 = 10x^2 + 21x + 8#
#10x^2 + 20x + 10 = 10x^2 + 21x + 8#
#10 - 8 = 21x - 20x#
#x = 2#
Hopefully this helps!