paynelove19
contestada

solve each logarithmic equation. Round your answer to two decimal places.
log4 16 = x
my attempt:
log4 16 (x+x) = x
--
x
log 4 (x+16) = 1
(x + 16) = 1
x + 16/1 =17
x+ 16 = 17
x= 8/9

Respuesta :

mhanifa

Answer:

  • x = 2

Step-by-step explanation:

Given equation

  • [tex]log_416=x[/tex]

Use the property of logarithm

  • [tex]log_ab=c[/tex] ⇒ [tex]b = a^c[/tex]

Apply to the given equation

  • [tex]16 = 4^x[/tex]
  • [tex]4^2=4^x[/tex]
  • [tex]2 = x[/tex]
  • [tex]x=2[/tex]

Let's see

[tex]\\ \rm\Rrightarrow log_416=x[/tex]

[tex]\\ \rm\Rrightarrow 16=4^x[/tex]

[tex]\\ \rm\Rrightarrow 4²=4^x[/tex]

[tex]\\ \rm\Rrightarrow x=2[/tex]

Done!