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a.- In x = In 3 + 2 In 4 - In 2
In x = In 3 + In 4² - In 2
In x = ln 3(4²) - In 2
In x = ln 3(4²) / 2
In x = ln 3(16) / 2
In x = ln 3(8)
In x = ln 24
x = 24
b.- (x - 1) log 2 + log 8 = log 4
log 2⁽ˣ⁻¹⁾ + log 8 = log 4
log 2⁽ˣ⁻¹⁾ + log 2³ = log 2²
log 2⁽ˣ⁻¹⁾ = log 2² - log 2³
log 2⁽ˣ⁻¹⁾ = log 2² / 2³
2⁽ˣ⁻¹⁾ = 2² / 2³
2⁽ˣ⁻¹⁾ = 2²⁻³
2⁽ˣ⁻¹⁾ = 2⁻¹
x - 1 = - 1
x = 1 - 1
x = 0
c.- log (x - 1) + log x = log 10
log (x - 1)(x) = log 10
(x - 1)(x) = 10
x² - x = 10
x² - x - 10 = 0
- (- 1) + √((- 1)² - 4(1)(- 10)) 1 + √(1 + 40) 1 + √41
x₁ = -------------------------------------- = ------------------- = -------------
2(1) 2 2
- (- 1) - √((- 1)² - 4(1)(- 10)) 1 - √(1 + 40) 1 - √41
x₂ = -------------------------------------- = ------------------- = -------------
2(1) 2 2