Question

Persamaan logaritma
a. log (log x + 3) = log 2
b. 4log2^x = x
c. 3log^2x-9.3logx-10=0

Answer 1

Verified answer

Jawab
a)

log (log x + 3) = log (2)
log x +  3 = 2
log x = -1
x = 10^(-1)
x = 0,1

b)
⁴ log  2ˣ  = x
4ˣ  = 2ˣ
x= 0

c)
³log² x - 9. ³log x -10 = 0
misalkan ³log x = y
(3log x)² - 9(³log x) - 10 =0
y² - 9y -10 = 0
(y -10)(y +1)= 0
y = 10 atau y = -1

y= 10 → ³log x = 10 → x = 3¹⁰
y = -1 → ³log x = -1  → x = 3⁻¹ →  x = 1/3
HP x = { 3¹⁰, 1/3}

Answer 2

Verified answer

A. Log x+3=2
10²=x+3
100=x+3
x=100-3
=97
b. ⁴log 2^x=x atau soalnya 4.log 2^x?
C. Misal ³log x=y
y²-9y-10=0
(y-10)(y+1)=0
y=10 atau y=-1
³log x=10
x=3^10
=3^5.3^5=243.243=59049
³logx=-1
3^-1=x
x=1/3