2.log(x²-1)=log8
3.²log(x²-2x+1)=²log(2x²-2)
Tolong yhh
persamaan logaritma
No. 1
⁵log (2x + 4) - ⁵log (x - 1) = 1
⁵log (2x + 4/x - 1) = ⁵log 5¹
⁵log (2x + 4/x - 1) = ⁵log 5
2x + 4/x - 1 = 5
2x + 4 = 5x - 5
2x - 5x = -5 - 4
-3x = -9
x = 3
____________
f(x) = 2x + 4
f(3) = 2(3) + 4
f(3) = 10 > 0 [{memenuhi}]
x - 1
= 3 - 1
= 2 > 0 {memenuhi}
HP : {3}
No. 2
log (x² - 1) = log 8
x² - 1 = 8
x² - 1 - 8 = 0
x² - 9 = 0
x² = 9
x = ±3
untuk x = -3
x² - 1 = 8 > 0, {memenuhi}
untuk x = 3
x² - 1 = 8 > 0, {memenuhi}
HP : {±3} atau {3,-3}
No. 3
²log (x² - 2x + 1) = ²log (2x² - 2)
x² - 2x + 1 = 2x² - 2
x² - 2x² - 2x + 1 + 2 = 0
-x² - 2x + 3 = 0
x² + 2x - 3 = 0
x = 3 atau x = -1
______________
untuk x = 3
x² - 2x + 1
= 9 - 6 + 1
= 4 > 0
2x² - 2
= 2.9 - 2
= 16 > 0 {memenuhi}
________________
untuk x = -1
x² - 2x + 1
= 1 + 2 + 1
= 4 > 0
2x² - 2
= 2 - 2
= 0 dimana 0 = 0 {TM}
HP : {3}
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