Question

resolva:
 log (x-3) na base 2 = 3
log (2x-4) = 2
log x na base 4 + log x² na base 4 = 12
log x³ - log x = 2

Answer 1

log (x-3) na base 2 = 3
x-3 = 2³
x = 8 + 3
x = 11

log (2x-4) = 2
2x - 4 = 10²
2x = 100 + 4
x = 104/2
x = 52

log x na base 4 + log x² na base 4 = 12
log x.x² na base 4 = 12 (propriedade da soma de logs)
x³ = 4¹²
x = 4⁴ = 256

log x³ - log x = 2 (propriedade da subtracao de logs)
logx³/x = 2
x² = 10²
x = 10

Answer 2

$log_2(x-3)=3 \\ \\ x-3=2^3 \\ \\ x-3=8 \\ \\ \boxed{x=11}$
-----------------------------------------------------------------------------------------------------------
$log(2x-4)=2 \\ \\ 2x-4=10^2 \\ \\ 2x-4=100 \\ \\ 2x=96\\ \\ \boxed{x=48}$
-----------------------------------------------------------------------------------------------------------
$log_4x+log_4x^2=12 \\ \\ log_4(x.x^2)=12 \\ \\ x^3=4^{12} \\ \\ x^3=16777216 \\ \\ \boxed{x= \sqrt[3]{16777216 } = 256 }$
-----------------------------------------------------------------------------------------------------------
$logx^3-logx=2 \\ \\ log\frac{x^3}{x}=2 \\ \\ log x^2=2 \\ \\ x^2=10^2 \\ \\ \boxed{x=10}$