- #1
Mootjeuh
- 5
- 0
Homework Statement
I'm trying to solve trying logarithmic and exponential equations but for the life of me I can't seem to figure out what I'm doing wrong.
Homework Equations
Log equation: log3(x+2)+1 = log3x²+4x
Exp equation: 2x + 2x+1 = 3
The Attempt at a Solution
For the first one, here's what I did:
- 1 = log3(x²+4x) - log3(x+2)
- log3((x²+4x)/(x+2)) = 1
- log3((x² +4x)/(x+2)) = 1
- log3((x+4x)/2) = 1 --Can I do this? Dividing the denominator and numerator by the same value within a log
- log3(x+2x) = 1
- log3(3x) = 1
- log33 + log3x = 1
- 1 + log3x = 1
- log3x = 0
- x = 1
And then for the second one:
- 2x + 2x+1 = 3
- I figured I'd put them all on the same base so I tried to find 2 to what power equals 3
- So I did ln(3)/ln(2) = 1.584962501, which for simplicity's sake I'll replace by y here
- And when I put in 2y in my calculator it does give me 3 so it must be correct
- x + x + 1 = y
- 2x + 1 = y
- x = (y-1)/2
I'm at my wit's end here, I don't know what else to try.
Any help is greatly appreciated.