logarithmic.py

Created by thabo
Created on June 06, 2024
846 Bytes
"""

log5[10x/3x-1] = 1
Remove log
5^1 = 10x/3x-1
solo the x
15x-5 = 10
15x = 15
x=1
YOU MUST CHECK PUT X AS 1 SOLVE

3-log2(x+1)=log2(x-1)
add log2(x-1)
3 = log2(x-1) + log2(x+1)
3 = log2[(x-1)(x+1)]
3 = log2(x^2-1)
remove log
2^3 = x^2 -1
8 = x^2 -1
add
9=x^2
root
x= plus or minus 3
CHECK WORK
3 works - 3 does not

log4(x-1) + log4(5) = log4(x+6)
combine
log4[5 * (x-1)] = log4(x+6)
log4=(5x-5) = log4(x+6)
remove log
5x - 5 = x + 6
-x 
4x - 5 = 6
+5
4x = 11
x = 4/11
CHECK   WORKS

log2(x+3) - log2(x-1) + log2(2x+6) - log2(3)
simplify
log2(x+3/x-1) = log 2(2x+6/3)
remove log
(x+3/x-1) = (2x+6/3)
* 3   *(x-1)(2x+6)
3x+9 = 2x^2 + 4x -6
-3x - 9
0 = 2x^2 + x - 15
simpflifiy
0 = (2x -5)(x+3)
x = 5/2 x = -3
CHECK   only 5/2 works

ln(4x) + ln(5) = 5
ln(4x * 5) = 5
ln(20x) = 5
e^5 = 20x
e^5/20 = x
x = 7.421
CHECK WORKS
"""