Question

Tolong jawab soal yang 5.b dan 5c.

Answer 1

5b) 3ˣ = 2²ˣ⁻¹

log (3ˣ) = log(2²ˣ⁻¹)
x. log 3 = (2x-1) log 2
x log 3 = 2x log 2 - log 2
2x log 2 - x log 3 = log 2
x (2 log2 - log 3) = log 2
x ( log 2² - log 3)= log 2
x (log4 - log3 ) = log 2
x(log 4/3) = log 2
x = log 2 / ( log 4/3)
.
x = ⁴/³ log 2

c. x^(2. log x) = 100/x³

x³ . x^(2. log x) = 100
x^(3 + 2 log  x)  = 100
.
log  [ x^(3+2 log x) ] = log 100
(3+ 2 log x) log x = log 100
 3 logx + 2 log² x=  2
misalkan log  x = a --> x > 0
.
2 a² + 3a - 2 = 0
(2a - 1)(a + 2) = 0
a = 1/2  atau a = -2
.
log x = 1/2 --> x =  10¹/² = √10
log x = -2 -->  x = 10⁻²  = 1/100