Question

Quiz Fun Math

Materi Logaritma

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Jika log (log x) = log (log (1 + y)) + log 2 dan log (x - 5) = 2 log y, maka x - y = ...
A. 7
B. 8
C. 9
D. 10
E. 11

silahkan ^^

Answer 1

Log (log x) = log (log(1+y)) + log 2
log (log x) = log ( log(1+y).2 )
log (log x) = log ( 2 log(1+y))
log x = 2 log (1+y)
log x = log (1+y)²
x = (1+y)²

log (x-5) = 2 log y
log (x-5) = log y²
x-5 = y²
(1+y)²-5 = y²
1+2y+y²-5 = y²
2y-4 = 0
2y = 4
y = 2

x = (1+y)²
x = (1+2)²
x = 3²
x = 9

x-y = 9-2
       = 7

Answer 2

Log (log x) = log (log (1 + y)) + log 2   
log(log x) = log (log (1 + y)) . 2                [dibagi log]
log x = log (1 + y) * 2
log x = 2log (1+y)
log x = log (1+y)                      [dibagi log]
x = (1+y)
x = 1+2y+y²


log (x - 5) = 2 log y
log (x-5) = log y²                     [dibagi log]
x-5 = y²
x = y² - 5           

penyelesaian

x = 1+2y+y²
x = y² - 5

1+2y+y² = y²-5
2y = -6
y = -3

x = y² - 5    = 9 - 5  = 4

x - y = 4 -(-3) = 7